Beginning of Section
CombUnif
Variable
X :
set
Hypothesis
HX :
combinator
X
Variable
Y :
set
Hypothesis
HY :
combinator
Y
Variable
Z :
set
Hypothesis
HZ :
combinator
Z
Variable
W :
set
Hypothesis
HW :
combinator
W
Theorem.
(
conj_CombUnif_TMS6V89Z4BVNbFaibAcpuMGG6pbcBerBebn
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
W
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
W
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
30abbf...
and proposition id is
022318...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWxmS5YNamHYfetXsEyGe8Fotr3jzkw89R
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
)
)
X6
)
)
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a93963...
and proposition id is
335af3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUtNaFAFPEjt9H7ck9oZsPAxRuDftJW1C1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
X
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
Z
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
X5
)
)
Z
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9b0e62...
and proposition id is
9af4bb...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFvMxDMuD16f7x7GcYcydj4QcqU2yCQrZD
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a09b8c...
and proposition id is
00e040...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSwGx6Zm95DQdK2YiS65ZGpTW3DSpPM9SH
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
W
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X5
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
Y
)
)
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
42eacd...
and proposition id is
4a71d8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdFjrXmGAtUWuwqJUyA4Q7X5RJFiRVupEj
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
Z
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
Z
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fe8beb...
and proposition id is
f6f3b9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJHuoFQGANuAGyPbBL7Fp3Kir4PZ6JtTFK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
W
)
)
X4
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X7
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
X7
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
Z
)
)
W
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
Z
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c66690...
and proposition id is
13a64a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNGyChKGEUkJavi6Bt5uXVXJJGi14cov2Z
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0d9a11...
and proposition id is
fb70ba...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGvk436hJd4iUEafss9Vvm6FFGm7U3rpzL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
Y
)
)
Z
)
)
X4
)
)
Y
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
X5
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
28c21b...
and proposition id is
18fb08...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKYLYJ5Kok2xvBRKR5J2d5j5YZUjtYGFCZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
Y
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5cfec8...
and proposition id is
1ee432...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUZRrkoyjQyxTdcHy56b7vB9dm7sarNFPo
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
X7
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X7
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X5
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a15213...
and proposition id is
1c507b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXq48A9aUyUARuhntu3V2i2CfmtJEzeDS2
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Z
)
)
X4
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
W
)
)
X
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6deddd...
and proposition id is
0533c4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMap9F47AzS5GWLNWGxK6uDUdyyv9eZMGwZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
W
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
)
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X7
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
X
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
251e74...
and proposition id is
235066...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcUzoG7LWBMgVtbqWrkHqJAwHwK3L4jUTb
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1325bf...
and proposition id is
effb50...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLXZEKpS6MEcjHJfr3ihcZvogXGQMCpFis
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
aad4fa...
and proposition id is
468b71...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFAs4YvRyjQzNQNNsotZD5nWLJAi3t6n3G
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
Y
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
21a08f...
and proposition id is
3fbd09...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMM6RRVQnGaZeE3rX7Hpqv9R7WxACTWhG6D
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X6
)
)
W
)
)
Z
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
X7
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f4698b...
and proposition id is
255dc4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMStuUd9wqC79mY18WhTPfXFuxdmr49ABpN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X6
)
)
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X4
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X
)
)
X7
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cf700d...
and proposition id is
b8a222...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMd5i8zVjppAGbcevy5KmRvW8LvzHUM7voX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6da2e2...
and proposition id is
ca9bd0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTBaN6QVvhnKU41BQFqLHokK5fK85vfXTY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9e64aa...
and proposition id is
78e516...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNrjZ6sjAgk4ozokEvvTvY1T1zQjAuPrcd
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
Y
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
029463...
and proposition id is
98302e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHoLosDwUTMYWMvEJAme37yWNAtFqgd8qj
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X7
)
)
X6
)
)
X7
)
)
X
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
241840...
and proposition id is
dfdc36...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMN6GJ3WPd2xV3T4ho1ZhuN5Enu6GqX4mHt
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
X
)
)
W
)
)
Y
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5099ff...
and proposition id is
5c99e5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYkedWKL4JHZQzTXiFttKvPpr9QhF7szbX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
Z
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
X6
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
X7
)
)
Y
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7e17b7...
and proposition id is
931dee...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMP9j27RbMCuzBrkFWLn2UMAKniZERT2V7F
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
69dcf9...
and proposition id is
ae92c1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMM4SgFZ9opSqy48LWZQ1MivAmN1Eg2ixjg
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X5
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e8df2d...
and proposition id is
4c5793...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLKiwwcUcdZvPoGvHkQZgPyvAE7GojN7Ka
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X7
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d54411...
and proposition id is
9f3316...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQXgTAJA5ifdmsRMdNvZRZVzFeKHR976TP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
X7
)
)
Z
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8cb3f8...
and proposition id is
ff0d92...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEsAoLvrNY93Z21UFPuhUp31E5ZeYzNLet
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b679f6...
and proposition id is
6973d5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFPACQnhAKJsqAgsDiPQEvoyXieu7Ppa5R
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
Y
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X
)
)
W
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e5c09e...
and proposition id is
87ace3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMawMjto8f1tbueQUnzkhBbapXNTurLQCfz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X7
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cf7ec4...
and proposition id is
79f434...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHumvynZD96hM1aX5pnZerFdfgzsoET7RS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
X6
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
Y
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
W
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
725dc2...
and proposition id is
c285ed...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaWhxqkahgBuW6ULhgq36KmPzjFFwXDdSY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
X
)
)
X
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Z
)
)
)
)
X6
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1003da...
and proposition id is
7bb6ad...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcrQFVGZjJ9UTNniJ6utVMAwCVXBMzKkLF
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
X
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
W
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
Y
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X4
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
83cd92...
and proposition id is
8af00b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaRawCefHM5f5eiPnQyBMHQh86np3yXfTq
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Z
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9c8d2d...
and proposition id is
c9d2f4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRPqxwdt55DhbYctBnmQeZLym1MX5vPQbp
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Y
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
15ef13...
and proposition id is
1b14df...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLyF3fVzyAKmwdcaTh3MM4FpsF1pHhcHgz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X7
)
)
)
)
X
)
)
Z
)
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
78e33d...
and proposition id is
825153...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMacfbVUJkCzkW5KN6zUAogZHXanHbQSykX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2ad713...
and proposition id is
332534...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNHfoJyFKYxoeFHvUCs518cBmos3Ay8zc2
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
Z
)
)
Z
)
)
X6
)
)
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
Z
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
W
)
)
X
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X5
)
)
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
07b646...
and proposition id is
a34245...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRZZPi3sqQFWRncgFPnpoTP4C4CqsABdTJ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
870074...
and proposition id is
0aeca3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVuqcufHsHvPe2ouXzEvBVjuYJ1K1bXxmB
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
W
)
)
)
)
X7
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
W
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b2eea9...
and proposition id is
0dfdd7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLcWpz6FsP1Ufk4kXeefChiZiCUNKpEvQn
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
)
)
X
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
X4
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7ed611...
and proposition id is
9b82f2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbupb35WzNjm797oGnHdKLfXK1RmKqEn6x
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
)
)
X
)
)
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c22291...
and proposition id is
ea7300...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMM5KnEpCiZ8S2mPzDWVepDW39cK3xVW3kH
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
X6
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b7c4f0...
and proposition id is
eb92f9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXWYpZQNURMX3mDGZpzeLkV9679cyJYXH7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X4
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
W
)
)
X7
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
X
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
56e3ca...
and proposition id is
03e675...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGgUtj13cY5QaoVybECjPWNn9ahrvPFunY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Y
)
)
)
)
X4
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X7
)
)
X
)
)
W
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bd47b0...
and proposition id is
af53ee...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFNPL9PAHsYLwioqsGShz9tJcmMZ8dhyfx
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1c911a...
and proposition id is
55303b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKK8GiH3Y7d5jYev4WMqGEaUgacEdiGb7K
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X6
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
X5
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
464e8d...
and proposition id is
f458c7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXjanXSBDsmkAEF19QE3w3VQoe5uC4wQs4
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
Z
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
)
)
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X
)
)
)
)
X4
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
Y
)
)
Y
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5f486b...
and proposition id is
92b697...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcUwQjo7LLFxdk8AbX2Bxjuhon742Gecn3
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X5
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fd09f4...
and proposition id is
b561ec...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWyWH177ymLzHK21MYy4vQcEo7L95P73qb
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
X
)
)
)
)
Z
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cfd4cb...
and proposition id is
a4ae7e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMwR4rqtfJw8gMTethjVY6T8zvSDp98kJu
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X4
)
)
)
)
X4
)
)
)
)
Y
)
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
X7
)
)
)
)
Z
)
)
Y
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Y
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
W
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d87c67...
and proposition id is
c3a7c9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdQZCATrDUPrXjjmpBDuXogV9RTNfSkjAi
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
X5
)
)
Z
)
)
X4
)
)
Z
)
)
X
)
)
Z
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X7
)
)
W
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
X6
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
X4
)
)
X
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5a077d...
and proposition id is
0ef1f6...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWhLRzrJN3nGCxHUFupkmGkjDUsRCa1zAY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
Z
)
)
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
Y
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
Y
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X7
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6a629b...
and proposition id is
c4ec1a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRFk5sJ4eV3yF5JwuZwQGTSXAyTyG1MWxK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1f9d4a...
and proposition id is
c3a6f9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHzRNq2zQcy8uhTuSePH7imtfbZmfvUnTb
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
W
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
W
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
W
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cc5e95...
and proposition id is
bf7d9b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTYWrx6TTUvuLmF2zTfYnRfha8F9i59SMZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
W
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X4
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e84628...
and proposition id is
2b458e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRxFESNV1LzhxHGoiRUmxkHg68iBh4s892
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
)
)
X
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2c3707...
and proposition id is
2f8c5d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJnS5Fdcp6K48dVW5HPgeWhbfvinZKMZyj
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X7
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1dec70...
and proposition id is
5f6919...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYcynj9HFs38iEfwoZNpwALFfwD6obfvYw
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Y
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
32d46b...
and proposition id is
2ccb7c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXjaqURy6Gyi8oZSetDnuGDue1vtDwokXK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X4
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
X
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
Y
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
09a6ee...
and proposition id is
7495a1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVTr26AxjNBE645kLyg28jh86AJ3Frr2Ge
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8d6f45...
and proposition id is
e7df97...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPheoapuXyDpRN3aXv4vXpea47kzvfNHJx
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
X4
)
)
Y
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X7
)
)
X6
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
Z
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
434d04...
and proposition id is
9bce51...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWprpCagH3cAVMWfZHzSnQYEuhDubWezYR
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
X
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
680d05...
and proposition id is
5d5904...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMu4epoMMqQcD8cqXxHKF7yo6MT3mRDK7X
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
Z
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
82555b...
and proposition id is
e8b8c5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPuk1EPtoSKH5MPFWcrCL2v5MwoZTSv7cZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X
)
)
X
)
)
X6
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fb7b26...
and proposition id is
e247e9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPrmXRxBJ3fdcfg7ZSCCPpRFroqxz2Hvwa
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X
)
)
X6
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
Z
)
)
)
)
Y
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
24f8bc...
and proposition id is
0688e2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbxgtcn3NEi1yUhEMXCty6EpFHcYqUiJQC
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9d47b6...
and proposition id is
d18cb8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbBbWzUkqG1syyVsWcH4eHu8vASq4WTUb1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X7
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e8c455...
and proposition id is
2fd2d8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMW9ScgYQVpkLqWKvFyuUbmGzF4NYYU1Kvo
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
W
)
)
X6
)
)
W
)
)
X7
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
)
)
X
)
)
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
25324f...
and proposition id is
ff2e33...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSrwWzztvxtAhc1T41ZaWEwmKec5rbgM9D
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X7
)
)
)
)
Y
)
)
)
)
X4
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a499cb...
and proposition id is
6592ef...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHdGHLzpYAtvj3tHDVMhzaLqErEGTjqudU
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
Y
)
)
)
)
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
Z
)
)
X4
)
)
X6
)
)
)
)
X6
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
64e5f0...
and proposition id is
8f4ab2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVfXtYSPB2kpzK3Ar7Tstg9Y7kdqtzix6F
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
X7
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
W
)
)
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1736ae...
and proposition id is
23be9b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMW1kx79KjjRTPFPt1dzJRYu2NiR2U2zFgC
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X4
)
)
)
)
)
)
Z
)
)
X
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
W
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ec074d...
and proposition id is
c3582f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTLdhfDXS1wkUoxBjKwsWhocrXD1oeGLHP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X7
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
W
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1bf973...
and proposition id is
fb8a03...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFEN2bM1WPL1ZKqPQV6h3sEsNmiKtGpnUP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
Y
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X6
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X
)
)
X4
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
699904...
and proposition id is
00c863...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEteC3qrJxP9vPUxp5wqryGdGS4YuzzN5Z
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
Y
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
X5
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f64779...
and proposition id is
87ea34...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFkAMksCBVio3HTuPnQ9X7bd1jx6Yh2nsu
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
Y
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X5
)
)
Z
)
)
)
)
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
)
)
Z
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
520cae...
and proposition id is
130d73...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYzgNynqVNxM5z5McSnpyja2VtwKUsqZ2e
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
76b366...
and proposition id is
943fa1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSwD1d5Z8g1Vz9kxc9TGNqAuHStxgvu85y
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
20fc74...
and proposition id is
1de005...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPFmwuQDEP6pRFWGHgapxUqj3KBa6YqJsN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
X7
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c70c93...
and proposition id is
ed6404...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXWFdcTsbAqbjiBUf2i5x6NnNvVHMAHf1Z
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
W
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f08d12...
and proposition id is
4e67e0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLdka8RoqEJCtV8qaidvHanLtnhqw5iNTo
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e67b5e...
and proposition id is
785d22...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMakikC5FS5e9QgZui3jwJ1kGV3UygG8T3n
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Y
)
)
X7
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
X7
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
X
)
)
X
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
773790...
and proposition id is
a91082...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTYAUZTPYHyUDbRkFy76xH41pNyqXNmGVJ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
W
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X7
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
Z
)
)
Y
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
X4
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X7
)
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
dc3954...
and proposition id is
5b0002...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMT8R7q55K3BpxZFJyDAAw9K7pzM93NFyYG
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
X4
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X4
)
)
X7
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
39cdc9...
and proposition id is
7ed722...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNkSTK63V5znZwdsQzrK84FcqUFwRzW7yg
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Z
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6d37a0...
and proposition id is
5f52c9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGPnhXyiqWhMFuiHzsuD1wDHHgKYnyZXLS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
X5
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
X4
)
)
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
dadae8...
and proposition id is
2b6436...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMch9ePP7HTZ7UTSLFwYGnXfFVwZipJc8Tr
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X4
)
)
Z
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
W
)
)
Z
)
)
Z
)
)
X6
)
)
)
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2ee663...
and proposition id is
09a5a7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMktK9Qk7qA5kGZNu1KXQrY7gQTPA5uNk6
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
W
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Z
)
)
X6
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f28c55...
and proposition id is
6b42bb...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXHv7tJzwDCgBfJhdh9zWHQQnMEdgvWDT7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8b2fc6...
and proposition id is
c708f2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFDuabjMSSC4fZMMP6iRjDHQnfJDNDC1dN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X5
)
)
X
)
)
X
)
)
W
)
)
X6
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
W
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d3290d...
and proposition id is
cf54f8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHoZSVqugRjDRdCDeMjLSxBD1UZzGGJr5Q
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
W
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3e5cdd...
and proposition id is
545160...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYe6uutpqcKjWyKcaV3R2SWpHL5Uqd64eB
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X7
)
)
X5
)
)
)
)
)
)
W
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Z
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a3ac58...
and proposition id is
0c3377...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMU2WxBwdWaFMCcjJuHMxnsdmJmZ27yyUPg
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
X7
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X4
)
)
X5
)
)
Z
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Y
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9c9fce...
and proposition id is
6f8520...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMQWY1iDAgKpngPUr3TkYQfFq6nQaJ2ABD
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
Z
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
)
)
Y
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bfec30...
and proposition id is
505704...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMayg1TiQUg6VeWf249LL46My343fe2ZPUg
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
)
)
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Y
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7b4e18...
and proposition id is
12fdfc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVq6pLdu4jSPb2FxtPiVi2HcMfajXkN6sR
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
253b09...
and proposition id is
bf4a2f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFZuZyHAACL3QJWeBfdY5Z3VvjAtHMAsvf
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X5
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
Y
)
)
)
)
Y
)
)
)
)
X7
)
)
X
)
)
W
)
)
)
)
X6
)
)
X
)
)
X6
)
)
Z
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
X5
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
64e698...
and proposition id is
ae5f56...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRvqcgXn8C3MfAFqkbAcFzdp2rn1Deftk3
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X4
)
)
)
)
X5
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Z
)
)
)
)
X7
)
)
Z
)
)
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9475b6...
and proposition id is
664c94...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPCetGskzeEwkisT9dgdJUjo3zFcUy8wss
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
Y
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
Y
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Z
)
)
)
)
X
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
abf611...
and proposition id is
66fa59...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMW3kY27XGf7S7Gy8mPMkzu1X1zzpM9Sic6
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X4
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
W
)
)
)
)
)
)
)
)
X7
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X5
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X6
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
X
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b26dce...
and proposition id is
8be4d5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVCSgyt6AUQyDFGLJhrZCeZomHT9Af5Lc1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3ea3ae...
and proposition id is
36ece0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQbN3NtnpL2bxRXx7dAmPV6VSBM1wNRyZ7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
X5
)
)
Y
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ca71b0...
and proposition id is
f6c537...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKQgLRVr2rcstMDgm9FwA2rNEKbKBrWRCV
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
Z
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X5
)
)
X5
)
)
X4
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
011a42...
and proposition id is
ffb32f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPjKw95uyMqLCoS3aKN1ocYd2hteb3VPQU
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
)
)
)
)
Z
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
Y
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a785ec...
and proposition id is
9a8831...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYXpTfA73t7kSwRDLTS4AsYKn73joDmFcp
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
942a3e...
and proposition id is
8ab975...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQHx9oeEBPMjRiSSzuXSoEnSkPTpGsmQ5q
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
)
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1441a3...
and proposition id is
e27158...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQSb3hdZks49QWpejoCa3mhDUT9chk2d53
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Z
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
X6
)
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
W
)
)
Y
)
)
Y
)
)
)
)
X
)
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
W
)
)
Z
)
)
Y
)
)
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bc1a74...
and proposition id is
5a86cd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbsXFZCQCM52XVvoTcJ6Qw6wCRnEUKX1k9
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X
)
)
X6
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
Z
)
)
)
)
X6
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
02aaa6...
and proposition id is
f3b15a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKHxCwmjrakTdFfgYmAwXWA2HzmYAUy8Lm
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X7
)
)
X4
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e80d55...
and proposition id is
1acfda...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMW3ATgLYBsWBHPED8UkPCQ3bRkHYhbecER
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
Y
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X6
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X4
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
W
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c99003...
and proposition id is
cc406f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZFZxicfk86YarBf6HtBurgKryCtRPduvz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
W
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
Y
)
)
Y
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
Z
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6349ca...
and proposition id is
ef0acd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMN7rKnGmQ7GoxpmcJnKGVVaCFUBLR9Vk6D
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
W
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9493ef...
and proposition id is
bc43c3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNcQEogytvMcDmD6AJrdoiZKH8YqAUEjyp
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X7
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
X6
)
)
X5
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d04461...
and proposition id is
23aee7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWcAa4in5xJ6dT8SZGhnUhZYy79YvAXypK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Y
)
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d61312...
and proposition id is
da5c9b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNRvaExUsUGo29i8UpFkG5qRr3Z9uJztn5
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
Z
)
)
W
)
)
Y
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
Z
)
)
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cba561...
and proposition id is
094392...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXhYbHJiVBES1q5Vo83m1BCTWwahne1guY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
)
)
)
)
W
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X7
)
)
Y
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
38c32b...
and proposition id is
378cac...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbDHf1hp7A2VzFCFa75gxNb8JX1JSK2ywF
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X5
)
)
X7
)
)
Z
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Y
)
)
Y
)
)
X7
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
W
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
X7
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
af3ca9...
and proposition id is
f3b7b8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKv4ZFzRrYrBYm3MpVrt4unRxrYbY4s2yY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
Y
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
X6
)
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
X6
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X6
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
Z
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
10dba7...
and proposition id is
414556...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKs6koTAaHSwHAqxvdVP64shhDAjUefLzG
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8ff2a1...
and proposition id is
a68e43...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMF5ZFy6tAzse1gHgHknQh3PMFWztfaaYyF
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X4
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
X6
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X
)
)
W
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
X7
)
)
X4
)
)
Y
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
da6f7a...
and proposition id is
475e4b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHUTFj2hGghy7Yy2xab88ii1EKJ7Fd4HiW
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
X4
)
)
)
)
)
)
Z
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
Z
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
acf111...
and proposition id is
4fe3dc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMU94kZbqSqcHzfjEqV4SqvEmRREnSP1LMJ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X4
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
W
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
X
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
366754...
and proposition id is
e8781a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZ5yZKFrzZDb62hLpQiQiRjZjhf6t8aLRA
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
Y
)
)
X
)
)
X5
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
baa43a...
and proposition id is
e4cfea...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUzxkfAao98U3bviWBVdKHckbsKRvfoTZN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X5
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
4141b8...
and proposition id is
6b6be3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTyc2nmpaev2WSA5CxTdrNgzpntapPDZzm
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
Z
)
)
Y
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Y
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
Y
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
X7
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
632002...
and proposition id is
765e73...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSovy7TTarSbZ7m6fP8oKFfBf5teCF8hkK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
Z
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
Z
)
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Y
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X4
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
85497f...
and proposition id is
aa91c1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcvu8PHtEaKLzSHFtHhEA25kqbUmGjf3dq
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X6
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X5
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
W
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X5
)
)
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e649cc...
and proposition id is
77e822...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMa3DWZjKQbdNSMFybFTEjB9hyMvne3c3Fp
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X7
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6b7aa6...
and proposition id is
f5dec0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTnxVXrqnbjtT1GtppJvsjvfeBdzsAJkn9
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
W
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X7
)
)
)
)
X6
)
)
X4
)
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
129c0e...
and proposition id is
c6daf4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKYcCEUkDhQ7k7LyB7mceLAm6oWiQC6HZy
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
X4
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
W
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bd40c0...
and proposition id is
1f30c0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUNqnipqQEXW5FQtUnp9HaCC2VB7ZjuKBE
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
Y
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0b8767...
and proposition id is
e0a776...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQct96ctyhBZtQ6nFSte1hc2Arb3gWjZ3E
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
X
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X7
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X6
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X4
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
X4
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X4
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c616e0...
and proposition id is
e65cbc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPx2JUoWGpR2AEpFvVpc3mHCwKxGCupsAK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
)
)
X6
)
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
X4
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
X7
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X
)
)
)
)
W
)
)
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3e827f...
and proposition id is
7256bf...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdMK4uW6GXRb8ss43KJgV6793WEDNdyJ8b
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
Z
)
)
)
)
W
)
)
)
)
Z
)
)
W
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bfde5b...
and proposition id is
c0f1fd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQwfjLsXF5o7SMucs1NGZwGcWWqKXfwTan
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X5
)
)
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
W
)
)
Z
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
X4
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c430b7...
and proposition id is
b6792a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVNBgYtovwmcU4UYPeV7noLAumDBjchiYP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X7
)
)
X6
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
X4
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7f0a42...
and proposition id is
ce6960...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaVssgeEbegPmxVkwAJbowA5qDJENQTJav
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
X
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X7
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6f1945...
and proposition id is
1b333b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWtA4TpYRgpsRbx1jJKuWsiCAtznaCNzUn
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
)
)
X
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f6deb4...
and proposition id is
288d6c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNv523hTZv5MAsYuYvcZ99HmxWXqJZULZy
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
Z
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
aa0bce...
and proposition id is
e13815...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVZc32FfTE9bDHAJkRrizUpzXLCkpyvuKf
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X6
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
X
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
Z
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
Y
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
Y
)
)
X4
)
)
X6
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
X6
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c9d833...
and proposition id is
c22809...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKqZvpZXkgUuD7Mdnoat1u7v9cnwvyt4Qu
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
W
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
Z
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
de01d6...
and proposition id is
8e6086...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMF1b2HK2CVPo5miTXpgi5VdFdLLp2hYhtE
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
X6
)
)
X4
)
)
Z
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9fc909...
and proposition id is
b27c4a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKmy39gLTS6g5MYGHoezzr3j69wZEU5NLL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
W
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
10af6b...
and proposition id is
678376...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHBXvYxAn3vtjMuv6dzbqMxUPuHUjE7W2S
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
X7
)
)
X
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
81ca82...
and proposition id is
387c6b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWPMbdjFET1ePvqz9zvwh7vesCnfjfhQ2P
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
W
)
)
)
)
X6
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X5
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2c5169...
and proposition id is
741b2a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWP4469H4QdJDqdAspi34nSukYtuaeKufu
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
W
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
X5
)
)
)
)
X7
)
)
)
)
)
)
Y
)
)
X4
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
977993...
and proposition id is
da2bc8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYA93evyPKpdQG4UM1gw22g8q5ou7jwXcz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cb24dc...
and proposition id is
e77466...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMrYWniRHWoz3XGK7HphW35fK47tZVKtGM
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d6bb69...
and proposition id is
22b71d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQcyJPDDLssuhw7sJyrea12RzSYUkivtAQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X4
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X7
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
X7
)
)
Y
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b1e29a...
and proposition id is
5ad8ed...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKbPYQdAgQfrdzEvb3ACaMZs2LZESntaVQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
X6
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Z
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
12defc...
and proposition id is
cfaa8b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcFvqWTuL2kGBPTca2MqZo7BV2jb29Pgdd
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
Z
)
)
X4
)
)
W
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
196c29...
and proposition id is
59928f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUhtNPrd8RgXg3pYUkx7QJHckGfQrt9mjN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
Z
)
)
)
)
)
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
X5
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
X5
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f0e6a8...
and proposition id is
2c2897...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbXvj1mJrYMxtfxZofbHPx7N8PqEixKFAR
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
X5
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
db9ebd...
and proposition id is
a8ee93...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPrtMQA64m9x8CBv5iw3GbW1RQFjwhnCXn
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
W
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
Y
)
)
)
)
W
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
df2f8b...
and proposition id is
41689b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNAcR92B1eeL5Rhd1SDazSvLF5X5aE2Bbt
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X7
)
)
X
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X6
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
X6
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ae4912...
and proposition id is
5c8302...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcCjPSodR8EoZHDJQVsywKfeWcvTjzErYu
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X6
)
)
X6
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Y
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
aa4553...
and proposition id is
8b1a40...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVpYbNbpDgnQ3nuqixUzKWuXzQAWUPhidB
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
Z
)
)
X5
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b59bee...
and proposition id is
1d1de0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMT5qEoeacfQCC8dP2Fb3e8VwmrAvkGStzo
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
28b096...
and proposition id is
1f560c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZ9pYe9CWLGEqAoAh2hKVaDMqa9zvqbhQV
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
W
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X4
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
21de38...
and proposition id is
dd820d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHNcBL28qBCRaubR6oWXehMPf2SHXUVkA7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
Z
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c67c7b...
and proposition id is
42cbe8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHjwBAZBSGaH76g7VXT7fFakc2YgRWyJLj
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X
)
)
)
)
W
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bd60fb...
and proposition id is
1c92f7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJfr6KNoHGqi38rSRyUaoaKcaN6NxT6V5x
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Y
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Y
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
)
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fadbee...
and proposition id is
b9a50f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRXcri184ydVbE6VbVMiPH8yv9E8Fj4qM7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
W
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X5
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ea762f...
and proposition id is
99318f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSBhyeJ3mmy9SA2bznUpTe1XZxPH7CSTPC
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
X
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
db3e1a...
and proposition id is
c1f2a7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUVqEHxa1mhMXjmK4Qcfx5gG4eDgt1JfEY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
X4
)
)
W
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
81c76a...
and proposition id is
93c9a5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRrFz3z2sQCqRqviEmfh6eSRsyMo7rg2en
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X6
)
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X7
)
)
)
)
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X4
)
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fc2708...
and proposition id is
2143fc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMV6H7QeDhBafAvApfTonXAzaV34M1DyyDd
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Y
)
)
)
)
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bc8118...
and proposition id is
111864...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMd5WWbuetX7WZUWkaAChsD714bdZx9Gry7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Z
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Y
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
X5
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X7
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2395d4...
and proposition id is
187d85...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKusKSwdgo9KrvQaYxvJtAVEygPfWPiWZY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
W
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X7
)
)
W
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
791c5a...
and proposition id is
f235f8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbKFH1W2zcXFES5GozcBWEBTBYRkfUUNR1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Y
)
)
)
)
X4
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Z
)
)
)
)
X
)
)
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
Z
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
X7
)
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3905c1...
and proposition id is
728b3d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEzkUfRLEmNsosDKB6sSJojTm1XoEK97w5
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fe73e2...
and proposition id is
0524f2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZqBVgNmVSsAWoi7uUghicxwL4VyEU2x3C
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
X5
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a5a66e...
and proposition id is
c27268...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVxtUntLTRGHrgGEhMwSBJXfhaFu6acQ6r
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
Y
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
W
)
)
)
)
X5
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
W
)
)
X4
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
173d17...
and proposition id is
a2f5c5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKkdj1i43FyezXRXAHdHGKSdHkZA7Dq1de
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
253256...
and proposition id is
04bbe2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRoWyJnBkwXhS2y6248xShy7S6CfE2B54M
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
W
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bb0bf9...
and proposition id is
a11f78...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJsNAbEHtoedgUeAevhZ3Bht83raqTuPz9
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
)
)
W
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
553b17...
and proposition id is
f10358...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJsNYVSGZXk3r5cBnYhdfTNc4ePQVQJmtZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
Y
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X5
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
645e28...
and proposition id is
037076...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKQhqyaGGnxrjK3fHcPEbjPxX9ZHaJEsXD
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
W
)
)
X5
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
)
)
Y
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
12adea...
and proposition id is
128902...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJSrLQ4oUsv8mMqNvRtKoBpq4qbGnaeXpT
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9037c9...
and proposition id is
75b914...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWKpVjfZ2H3f2jVMTgF2MWemVcX5C46gKQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
Y
)
)
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X7
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
Y
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0a0a60...
and proposition id is
94852b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNek7Muz5CiLMzPnEawwXQFy9LM1JhLRnR
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
Y
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d783e0...
and proposition id is
f475c2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNDfM1rB3f7wsqu1akek9TQ9kgQXBvaGdt
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X4
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f57620...
and proposition id is
be29d5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMG19s8SZiW9t8z1faZkn5TW7GsafHDQoTL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
X7
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Z
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X7
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0098a6...
and proposition id is
f3f3e5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMd5F7S9pw27FE3PekbQiR1LH5Nmjxkgeaa
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
)
)
X7
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X7
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c469ce...
and proposition id is
b0f3c9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPRmtDpzwRpo7Up4VL7pCSS5ckcEzEVd63
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X
)
)
)
)
X
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
W
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
X4
)
)
W
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ab2eb0...
and proposition id is
37582a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPTXM3sPr6Sb4JCCrBBc41dfgHMVz9Vq7W
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
X4
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
W
)
)
)
)
)
)
W
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
)
)
X5
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
57c6c0...
and proposition id is
c6f615...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUWE9gheEfEVJZvyS6687iNpctoxbpD8iM
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
W
)
)
X5
)
)
X4
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
X6
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
Y
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
W
)
)
X6
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X7
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
57aa9b...
and proposition id is
eae0b7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdJChxitcGSM9gPLbsf21vvZPb4NkaETtL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
X7
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X5
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5f819c...
and proposition id is
affc56...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNCJAVwKLhEtadPaJCEwwTLJwrXsmdJ6n4
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
W
)
)
X
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
X5
)
)
)
)
X4
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
738a93...
and proposition id is
d77106...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEy7GJsaW3MyHYNEaiPQ2BMmEzHcAeyQ1W
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X4
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
Z
)
)
)
)
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
)
)
Z
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fa61f5...
and proposition id is
a49bad...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TML2Kg9KNGgT53Ujbqg5ErSqo55HK2MJdR1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X
)
)
X6
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X7
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
820f31...
and proposition id is
7c50ae...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMU18Z143iZZid4mRWX3PQprRXiUigrwvYP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ce340d...
and proposition id is
1fcadf...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUms2AC8a3TEvMgBBTenvimyVkiwkymY8a
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
Y
)
)
X7
)
)
)
)
X7
)
)
X6
)
)
X4
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
X
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X7
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
38d9f7...
and proposition id is
f56aec...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVNTYFB3f3MkmFmCjNGpMVZqe9b33K9pN8
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X6
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
W
)
)
Y
)
)
X6
)
)
Z
)
)
)
)
W
)
)
X
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7364e1...
and proposition id is
4780f7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQ82Nbm4RM4D7JJfn5ffYYqWm64pW7h4oW
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X6
)
)
W
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X6
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
X
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f46c63...
and proposition id is
17391e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXn7JmRpCRg2sb28LJsdh3CwvWNSrbr44n
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X7
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
X6
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
W
)
)
)
)
W
)
)
X4
)
)
X
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
Y
)
)
X4
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
120e38...
and proposition id is
96feed...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKFSERcwTFvfqM3X4nKtGHowmeQMPyteDf
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
X4
)
)
X5
)
)
X
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X
)
)
)
)
X6
)
)
W
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
Z
)
)
)
)
W
)
)
X
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6e3f4b...
and proposition id is
0e45b6...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTagmWbHhpnuHEsnok6xvWczShZxpRyNZy
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
X5
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
X
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
X6
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
537aa7...
and proposition id is
5f8286...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRUL4xymgLNdYSM61fjAfmsR7ZXqzCVwFS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
X5
)
)
)
)
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1365e0...
and proposition id is
5420d0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRPt7QF2xrE2USGo2m2DvNvPbPNeXG3uf1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bd317f...
and proposition id is
a8a60d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbpAhFPDXkevYU1XqVo54afki6yten3SYE
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Z
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9ebcd5...
and proposition id is
402a6f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPBf9uZ68N6jHmK7XM8cWLn57wnYz2VisK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f3be25...
and proposition id is
9b7abc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMb3kt67SmWvQk37ds9fY6skEEtEU47t1mh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X7
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d5c6b8...
and proposition id is
e3062a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMQXqPe9ZL6mAQ6ERXdBmi8hKYHnGx3Xf7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
W
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
Y
)
)
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
X
)
)
W
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
W
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
Y
)
)
)
)
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X6
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8acbdf...
and proposition id is
1af755...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQEYmDEiKMtHtHDv3o5XKSrJZHF6FkajGo
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
X6
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
X5
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
360856...
and proposition id is
4d62f9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJhTtXpjKoj5BrVRzGmFUq25KXDugvKnzW
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
X7
)
)
X6
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
X
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
X5
)
)
Y
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
W
)
)
Z
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6d5263...
and proposition id is
51967f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGmKeHjEMnjAwTvyGXneEb2w2kyx3JjfFz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X4
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X4
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
Z
)
)
)
)
X7
)
)
X6
)
)
X7
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
74d948...
and proposition id is
5ac035...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSFhE2w8M9J4Gj5xHwi2Ncw4Vnbp4sEree
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
X5
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X
)
)
Z
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X4
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1a1623...
and proposition id is
2c1a4f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdCyv6FVQD9CNJsQeMuzBLAEkHP8cRDVy4
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X4
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
20341d...
and proposition id is
b89523...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWVAyhy9T8r51WWmKXJdKFFrA6FirihUYs
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X7
)
)
)
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
X7
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
73d268...
and proposition id is
6e96f9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZ4f3JQfqXT2ToRHqgH6kL6atiDg5wg79y
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
W
)
)
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c7f009...
and proposition id is
d91e41...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcKGe7aTsRVAJcybycv8w27kayBwf8wkXX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f73575...
and proposition id is
a086c6...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMazYSSXC62ZVf8ZsQBfGSu6kr6T8widDbw
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
Y
)
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X
)
)
X4
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X6
)
)
)
)
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3506aa...
and proposition id is
8529e1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMb3nzFEfcfkdADZaY2fEU2WdpFEqwDQJr8
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Y
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X6
)
)
X4
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
W
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e82064...
and proposition id is
4d4f06...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYeQYVTBipCbrFr5hiy6hWaqJLwv1H4csK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
X5
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ee1649...
and proposition id is
e4de9a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbKPAiXKGi5DDn7VnsyAsAjBNUVyn31Bex
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Z
)
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
W
)
)
W
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2f3586...
and proposition id is
951471...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaCmJeV1rdqaXPPdkjqmduvcFvqHZSzxdc
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X4
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
X
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X4
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fc1d94...
and proposition id is
fe12e9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGbsuiU1bWkiXs5xpagD6b2AbQDRHvYuT3
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
Y
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
W
)
)
Y
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3aa650...
and proposition id is
da08d3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFYdpujFR81urK28eouRfvUbgUUUoQe3kS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X
)
)
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
Y
)
)
X5
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X6
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d806f9...
and proposition id is
ef9ae9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMt6hAa67mPJ3epaFrdGyWGxprBLBXiWZd
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X5
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X5
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3b5797...
and proposition id is
5d37a0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNF5nzMDQHWHavjsDgXFy3dM62TBLz2Phm
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X
)
)
Z
)
)
)
)
X5
)
)
)
)
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
X5
)
)
X4
)
)
X6
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X7
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
W
)
)
)
)
)
)
W
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X5
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f07f1d...
and proposition id is
6ac51e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbM69wPaPahoVpZy7UD5Z2wLd8fyjf3gBY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X5
)
)
Y
)
)
X6
)
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X
)
)
X7
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7ebf6e...
and proposition id is
1a0cb8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLSC7CfqKx4MDQxaUoK9DMRZxF6UeoKdpR
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7f2780...
and proposition id is
9a63f1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJNisMrBKnsoBnjmiRke6dun9uzvKrLxVX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X6
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
X5
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
Z
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X7
)
)
X6
)
)
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f3666b...
and proposition id is
40342c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUDKrbKJWhDugfyqrs5sxYtDUwxpMoKYpw
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
W
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Y
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
W
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
W
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
4e7896...
and proposition id is
dbc1f2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLVnVLSSuDn2eofatk1wMKU5Rhj8UcBzA6
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X5
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X6
)
)
X4
)
)
Y
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
541535...
and proposition id is
a7dc78...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXD58VBPi8onhWiJy7spg6XShRLkTjEjBQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X4
)
)
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
X5
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
fc18eb...
and proposition id is
5b1ea3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdGZQBhkF59bY6aiEENzJV4Dzt5RLWM5Ug
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
W
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X4
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
Z
)
)
X6
)
)
)
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a99454...
and proposition id is
74380e...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGQHXH965wkWqNeq47NcZVMP6A8nmTshsY
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
Z
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
67af10...
and proposition id is
7f6082...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEgND4Tvndiw4EdANvPvBuxnoKjLWG5Fqz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X7
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X7
)
)
Z
)
)
Y
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
X5
)
)
X7
)
)
W
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
X
)
)
)
)
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b4efea...
and proposition id is
96b0db...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdbpJBCsTvS9eoU7t8tLGgYsofEWPWxgtK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
W
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
Y
)
)
X6
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X6
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a0cc07...
and proposition id is
fac96f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNhLPFCYabLPER8qCGRYKPgsP5mFavBc5N
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
X6
)
)
X4
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
190e41...
and proposition id is
fed68b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMVhznQTfwsukanWKExpYgFQjSNiGxJuT93
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
08a220...
and proposition id is
d6542a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSh9tB18kbNHKc7n2jdvjYTMuyZmAVwjbS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
Z
)
)
X
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c68e12...
and proposition id is
4cd26d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSGCeYi17JA7RNRCTGZWu94YSjixZ2FMgj
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
X6
)
)
)
)
X5
)
)
X5
)
)
)
)
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
dfb661...
and proposition id is
3291dd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSSrRpYrUW6vm8G85CiqgTc8tMoiGRG5qr
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
Y
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X6
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7743bc...
and proposition id is
20eb27...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPJCz2pkEhWPjqy4kcpZagGM8QUxDMDLNq
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
Y
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
90fc1a...
and proposition id is
60abb7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMddoxvjhJJyuJMokZub183X1A5mFbBQwLE
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X
X6
)
)
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
462285...
and proposition id is
970948...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbSCx9qcaw5sjgucryNcGjMyGLmkL8TSJX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
Z
)
)
X
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6bbe40...
and proposition id is
0ebf67...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWnB6MpYpZ1ru6jjYUQTintiY1ztXqFs4p
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
W
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X7
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X
)
)
X5
)
)
X5
)
)
X5
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
X5
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ce4f05...
and proposition id is
90981c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTDdD5TcRR5uBFGbNdh7xKwFgozfhiXcfS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
X4
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
)
)
X7
)
)
)
)
X7
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
X7
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ce201b...
and proposition id is
90ded1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPiDh51CpGWUcRC4bkMEBrtGEv3stom7ac
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
W
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
Z
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d109ea...
and proposition id is
6c2403...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZFDQNFepVUYw7fMrpDsLpFZS3xuoEF9j9
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X6
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
Y
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
X6
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
21dae2...
and proposition id is
935daa...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXK1Yh7MV84CG8Xr7nvm2R6f6buPaD2YY8
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X5
)
)
X7
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
W
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0fcc04...
and proposition id is
c73853...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWBTY6JCmPFj8h8gruEijsZZj6ikCFDaup
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
W
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
X7
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X7
)
)
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7bec78...
and proposition id is
8fdf19...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXqDUTjcnNnSDCHUAzUqKq3YgcAr9D2ibB
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X5
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X
)
)
Y
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
X5
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
030c25...
and proposition id is
429422...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdsY9j136YcMCcV1cwKH5pG3MJJukYcSg7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
X5
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
438781...
and proposition id is
bc8666...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQgd3toaxhkh1tRjejBNm1qdThJ5euiwbh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d3e23a...
and proposition id is
4c48d7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcAa65UQQ1Gz7J9tRKNR3ZXb3EhGftmct5
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Y
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f671cb...
and proposition id is
c5f4e3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSSsA1kx7MDYkRs3cjjgJeLjxvYH4TRgSe
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
78af03...
and proposition id is
e830e9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLyrp7qx88QhRECCRfyDV7aL49PFWG3CFh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X6
)
)
X6
)
)
)
)
X
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
45429b...
and proposition id is
5a3976...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSu2K2qfG1bqvoTLSKVxCXAHY911TdAsBi
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X4
)
)
)
)
W
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Y
)
)
X
)
)
X5
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
4bf15e...
and proposition id is
9cc914...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYTom7ChggacUBgJJDzoWiWNmaZq5if5nt
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
W
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
34fc7c...
and proposition id is
4752b9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMXZAR3PK4jq7Bzqrvw6E3qYjaxKHFV79NZ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
X5
)
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
W
)
)
)
)
X
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0cbcd6...
and proposition id is
e6faa4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMM5CWXXU8TQNpJSkqMyxCX2W7QFjZQRKKh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
X4
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
Y
)
)
X4
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
X4
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a344bb...
and proposition id is
6cafe6...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMc96a3pz3vnu6vBngaf2PeXitSYfPh3XDv
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
X
)
)
)
)
X5
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
W
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
878cd1...
and proposition id is
5667c7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNeuJyCGDPRrBgbA54PV3XEbEnWg87iEue
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
02ead4...
and proposition id is
68b89f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMyKSyppUCFWaSt16UgaUUCaWPgKN1vmcP
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
Y
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X7
)
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
d162ea...
and proposition id is
d45c27...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMpxysbL3MFqNksPH7ppMt29BidqvzmX4o
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
Y
)
)
)
)
X7
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
40753f...
and proposition id is
75f474...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHgTfQNipTTPckUPA2MKqodY8ruzmtfEM1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
W
)
)
X
)
)
X4
)
)
)
)
W
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Z
)
)
X
)
)
Z
)
)
Z
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
X7
)
)
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
X
)
)
X5
)
)
)
)
)
)
Z
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
70fd38...
and proposition id is
2240fb...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFu7TWsS36qG8qxmjp3GVPQeLiqikP6bnD
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
X6
)
)
X4
)
)
)
)
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X5
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
42a8b9...
and proposition id is
c6c1b9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMP79VcPimyvfjPdvqYrc1WSGGMW6atgEQq
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X
)
)
W
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
X4
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
76a916...
and proposition id is
39adb8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMNPyUxVRHgD8t9AFPqdLUNB6MNjRXF9FQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c8895b...
and proposition id is
a792ce...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMU5mw86UtnaQZfFkJNHrUNk8undoMxCqsV
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
08b344...
and proposition id is
fd261f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZbkZLYsXsUTKbPM8Rnw5388zwS7QhrDpa
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X6
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9021b9...
and proposition id is
6a60b8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHZz1xGoqbSb3SMkXLbzuorJ1Bdenp4SW9
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
W
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
Y
)
)
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
X
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
W
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
bea86a...
and proposition id is
9a3e65...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMR69B7x1KKx68b9S6VMjG6UtofsKrwAgFv
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
W
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X6
)
)
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
X5
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cc75d8...
and proposition id is
f94343...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMNtSQNfrNWsL7KtfgoE8qMN8pSJYmDbBjS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
X7
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
X
)
)
Z
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
80cb81...
and proposition id is
c804f0...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPYQt7yfjeqCtgXWgDSefrMaWij81suU45
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X7
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Y
)
)
X6
)
)
)
)
W
)
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
X6
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
1a1b3d...
and proposition id is
db712a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMa4vaYoJB7pqynM6LL3LHNgxy9MdtF3dLJ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
Y
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
099037...
and proposition id is
b133b2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKpDJYeCQbxW4er8z2ccKA7RWigQLRVhQ6
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X6
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X6
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
X
)
)
Y
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
)
)
W
)
)
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9bb66d...
and proposition id is
5c9b92...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYNquoiUfpn56HRzr7raWj8VAXn41T4bfn
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
X4
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
3b9632...
and proposition id is
4a2b72...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUTMELLFTVQD5iWP4AaLBBgMt2LXvbtWRy
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X4
)
)
)
)
X7
)
)
X7
)
)
Z
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
W
)
)
X6
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
X
)
)
)
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ead927...
and proposition id is
207ac2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaY9WZSULvWt7TaX5r6K6zGKRMFBFezgge
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
)
)
)
)
X4
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
Y
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f2c71c...
and proposition id is
f46140...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMKcFWe4bLpX9NAyzSJifWNqB6QeomKDgue
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X4
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
X
)
)
X4
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
X5
)
)
Y
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b453c4...
and proposition id is
af4476...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTpNtYXWJmBwmW9AAZ8Th7eDcxvNX8EyJ1
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
X
)
)
)
)
X
)
)
X
)
)
Z
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
W
)
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
X4
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X7
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
X6
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X5
)
)
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cee92d...
and proposition id is
5d85f4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQhULQchRYSsWUAqbnbbFQowbD5Vz4mMrr
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
X6
)
)
)
)
X7
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
4100a0...
and proposition id is
26445a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYVesyJcfVbUReQjXp2tWQuLt75RhZxVUX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X
X
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
X4
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X7
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
Y
)
)
W
)
)
W
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
Z
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7ee6ae...
and proposition id is
14ab6a...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFWHuWfZbSfh3Lyo8FtxCaEhM5iD6cve9U
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
680716...
and proposition id is
6142e1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUPVPBfKpR2eEqZTef5uinomryWnmcnhty
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
X
)
)
)
)
Z
)
)
)
)
X
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X4
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
W
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
W
)
)
X6
)
)
)
)
Y
)
)
)
)
X6
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
cd0295...
and proposition id is
7e80e4...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMav1dE4LqHvVQZfA5Ntj2yDs5WJSQZ89So
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X6
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
Z
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7109d7...
and proposition id is
81bbd5...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJp93KTxyhcjucRLQe45qJ9pB1edBEzEZG
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
W
)
)
X4
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Z
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e8ffa4...
and proposition id is
58a88b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFad6yJUFXMxMYj7BtPdgaQwNZkwtRVgwh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
Z
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
W
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
X
)
)
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
X5
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
Z
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Z
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
aab9f0...
and proposition id is
3cdf93...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMbpCLK2AyrP1RvxyBqrZx6Sd3rv84jvkHy
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
X7
)
)
)
)
X7
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
W
)
)
X
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
Z
)
)
X7
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
Y
)
)
W
)
)
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Z
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
337801...
and proposition id is
48c9b3...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQ2nGfLLZ6Rab9X67Ttj4q4jNtnqiaj2E4
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
X
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Z
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
91ca89...
and proposition id is
0cbff1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLTfbBkhdDrc6NSCgnfTGVGuHgJ11vjh8N
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
Y
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
X
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X6
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
X
)
)
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
628ead...
and proposition id is
98aef8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMMEhoUvBdpXpqCwuCiWJoKB8PQ86KBuEo7
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
W
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
W
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
X
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
X6
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
63dddf...
and proposition id is
13aafa...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMUgMefdC3kN1YjwCcv1XCfgh7s5doLKXxN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X6
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Z
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj1
(
setsum
X7
Y
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ab1140...
and proposition id is
e40079...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTuxJhxsfpbetfyEoKEeqbMkd3brSzksDh
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
Y
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
Z
)
)
X4
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0e294b...
and proposition id is
40983c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWVBBU3AZMFYRGirAejdvu4u7MwrMXvtUT
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
X6
)
)
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X5
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
Z
)
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
Y
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Y
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
W
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X5
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8e8117...
and proposition id is
2bdf30...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPmCcyRiZJHxzXvLjeAEVZcTEPq4EU4DFb
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
W
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
Y
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
155c61...
and proposition id is
b4d1dc...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQRknwdtjW5ZXRouzdkm8RUceKWGT5JQZz
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
X
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X4
)
)
)
)
Z
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
dd1546...
and proposition id is
40566b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMR7R4XqDdgneRgAZgMmHoqw9xzjYH4iC3e
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X7
)
)
Z
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
W
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
640119...
and proposition id is
a17451...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMV9eyPQePnLFBn9BAgKYefk3Bf7UvM4ag5
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
X5
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
Y
)
)
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
X7
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7a8f77...
and proposition id is
dd68b9...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMF6Yy1bDLfnxgcMSMNb56EmuYVzvnWwRL2
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
Z
)
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
Y
)
)
Z
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
X
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
Y
)
)
X5
)
)
X6
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X4
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
W
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ca5fcc...
and proposition id is
29d7bd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMYrzD5abhvpUC7ghRBq8VVqFvi4GGALW4i
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
X6
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
57f657...
and proposition id is
8bc021...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMEqPo67XMDgQCHq3Y3wEbZyvZG4FY1RVqC
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
X
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
X6
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X6
)
)
X7
)
)
)
)
(
Inj1
(
setsum
W
X6
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X4
)
)
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
4e15c5...
and proposition id is
6d278c...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZzLfw5rQcc38NfiuMh9vqNfh3q9etbYu5
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X4
)
)
X7
)
)
X5
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
Y
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
X4
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
X6
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
X6
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X6
)
)
)
)
X4
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c9e777...
and proposition id is
ce1d86...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMRDz6EGS7JE8FZ8Lex2hyWveGDbw2Y4foC
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X6
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X7
)
)
X
)
)
(
Inj0
∅
)
)
)
Z
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X6
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
W
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f9c8d2...
and proposition id is
9b0696...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQWvEvrdGL9fJUgcBVGxFxVNSAj7RzjEsX
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
Y
)
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
W
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
X7
)
)
)
)
)
)
X4
)
)
)
)
Y
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
Y
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X4
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7103ea...
and proposition id is
903447...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcDN8JB7NiFiacU5MeRNUJiP6ynCmUjPHv
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
W
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
X6
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Y
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
X6
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
X6
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X7
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
066a05...
and proposition id is
8fbd70...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMFhPmXKim4k5x9cgNsbZJwFjXaTMwDKeqF
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X6
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X4
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
W
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
Z
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X7
)
)
X5
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
220e76...
and proposition id is
95c423...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGiZy2WA53GzjekrCyKXvjToxnxwxM89Cr
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
W
)
)
W
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
W
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Z
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5a0132...
and proposition id is
675245...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaZnJyW4JwWK2onST2Wv8BPo1peN9SDPSQ
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X7
)
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
Y
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj1
(
setsum
Z
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X6
)
)
Z
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X5
X7
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9d2c85...
and proposition id is
c493ce...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMLhUBgTkGKMSW5Ut1mbbY53LRyMde1Ae4b
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
X5
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X5
)
)
Z
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
W
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
Y
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
X4
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7d7d26...
and proposition id is
5547cd...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMHGFyt4ibmEJuQiuE7sHz2f3Wd3p1UoBSp
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X6
)
)
)
)
X7
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X4
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X7
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X7
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
Z
)
)
)
)
)
)
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
0401cf...
and proposition id is
8732d7...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMdn98hncdNVq46WDqpg7QfGL3zDvBEXe5w
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
W
)
)
X
)
)
X6
)
)
)
)
Z
)
)
X7
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
X
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
W
Z
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
362def...
and proposition id is
b3de45...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMSPD25G9LJAwrEYAJQiFE4SbtNRTxi7q9u
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
X6
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
W
)
)
Z
)
)
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X5
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
30a25c...
and proposition id is
7827eb...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMH67uuHZu3svdpfaaQ6iP6qrf1cBbrjYKw
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
X6
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
Z
)
)
W
)
)
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c1ca7a...
and proposition id is
15117f...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMQC5NiutP4xbN92q3sbho8XNSociD5ZYRL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
Z
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X6
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
Z
)
)
)
)
)
)
Z
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
9fe924...
and proposition id is
5b3262...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMaZXB9nYq6awMfGExbNn8QEJom4SBjBwwS
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X7
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
W
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X5
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
6adf7b...
and proposition id is
1835f2...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGQw5zanAURwwFHZvFjoZ6Sp2qDqZfdNFe
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
X7
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
W
)
)
X7
)
)
)
)
X
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X5
W
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Y
)
)
X5
)
)
)
)
X4
)
)
Z
)
)
)
)
W
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
X7
W
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
Z
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
X7
)
)
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
Y
)
)
X7
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
e66fb9...
and proposition id is
80f298...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPbAfvvVD5ugF1PiYQaBAogVShNttrd5a4
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Y
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X7
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X4
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
Y
)
)
X6
)
)
X7
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
X6
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
Y
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
a62b55...
and proposition id is
53155d...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMcGdqP6MxReq2bJ9bZxtLNqw1M42owbFHK
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
Z
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Y
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X7
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
X4
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X6
X4
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
Z
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X6
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X5
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
X6
)
)
Z
)
)
Y
)
)
X4
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
W
)
)
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
2757e0...
and proposition id is
5c1486...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWPjqLLzH7QyzaaQEctLsU6Uvd4Qaj8zX6
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
X5
)
)
)
)
X6
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Z
)
)
W
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Y
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
Y
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Y
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
X
)
)
)
)
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
X
X6
)
)
)
)
X
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X5
)
)
X6
)
)
X6
)
)
X6
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c2c09a...
and proposition id is
87bf2b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMPRJ9EFQDvVnsA914m8VEgEcNxZGZc8zkH
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj1
(
setsum
X
X6
)
)
)
)
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
W
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
X
)
)
X4
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X5
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X5
)
)
X7
)
)
X7
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
c8186d...
and proposition id is
151919...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TML4fMht1wFdApWxSN7BRyyvk4aHRkAHQMN
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X5
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X7
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
X5
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
Y
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X7
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
X5
)
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
Z
)
)
)
)
(
Inj1
(
setsum
Z
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
X
)
)
X5
)
)
X6
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
W
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
X7
)
)
Z
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
X7
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
5bc165...
and proposition id is
a404a8...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMV22bxdh2nt2Y2FZkNnQz8aeZAsRhm97U2
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X5
X5
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X4
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
Z
)
)
X5
)
)
X5
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X5
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
W
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
W
X
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
Y
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
X7
)
)
)
)
W
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X5
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Z
Z
)
)
)
)
)
)
X
)
)
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X6
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
49c1aa...
and proposition id is
687c12...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWL4S24iiXLFreWxftEvhkzD86WhEnaZnr
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X5
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
X
)
)
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X5
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
Z
)
)
Z
)
)
X
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
X
)
)
(
Inj1
(
setsum
W
X7
)
)
)
)
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X5
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
X5
)
)
)
)
X6
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
W
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
X6
)
)
(
Inj0
∅
)
)
)
W
)
)
X7
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
W
)
)
X7
)
)
)
)
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X5
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
W
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
X6
)
)
X4
)
)
)
)
Y
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b78adc...
and proposition id is
d86304...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGDXye5Tbt59t7SHB5tVR1wajz5HNVTMds
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
X6
)
)
X4
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X6
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X7
X5
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj0
∅
)
)
)
Z
)
)
W
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Z
X4
)
)
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X4
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X4
)
)
)
)
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
)
)
X
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
X5
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
X4
)
)
X5
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
W
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
f34849...
and proposition id is
c1ca92...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMZhqLprR1krSYvNdKE67t1Kp8HL923FDdT
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X7
)
)
X6
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X5
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X7
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
Y
)
)
Z
)
)
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
Y
)
)
X
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X6
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X4
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X4
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
Y
Z
)
)
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
Y
X5
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X5
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
Z
)
)
(
Inj0
∅
)
)
)
)
)
X6
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
X4
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
7243e5...
and proposition id is
c222f1...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMWfJE44yro72EzW2D3jRdM92afqoby2jVF
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X6
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
X7
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X5
)
)
X4
)
)
X5
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
X7
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
Z
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
Z
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X7
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
W
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
)
)
X
)
)
X5
)
)
Y
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
Z
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
)
)
)
)
Y
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
X7
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X5
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X6
X6
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X6
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
X5
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X6
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
Z
)
)
)
)
)
)
X
)
)
Z
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X7
)
)
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X7
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
Y
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
X7
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
X7
)
)
Y
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
ed7f57...
and proposition id is
83f6c6...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMGTKTsD5ptWMg69ExDnazF5WX9qnBnG8HL
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
W
)
)
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
Y
X4
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
W
)
)
)
)
Y
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X5
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
Z
Z
)
)
)
)
X4
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X
X5
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X5
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
Y
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
Z
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X5
)
)
X7
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
X7
)
)
Z
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
(
Inj0
∅
)
)
)
Y
)
)
Y
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
)
)
Z
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X5
)
)
X6
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
)
)
X4
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
)
)
Z
)
)
)
)
Y
)
)
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
X7
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X5
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
Y
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X7
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
X7
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
Z
)
)
(
Inj0
∅
)
)
)
X4
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
X6
)
)
Z
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X6
)
)
X7
)
)
X5
)
)
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
X7
)
)
(
Inj1
(
setsum
Z
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
b1e6d8...
and proposition id is
b32b5b...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMTUKN8RgUA1NvFwziUCv9RYU9ozcNpyiQ3
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X5
)
)
X5
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
X6
)
)
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
W
X4
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X5
)
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
W
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
Z
Z
)
)
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X4
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
X6
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X6
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
W
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X7
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X4
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X4
)
)
Y
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
∅
)
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
Y
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Y
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
(
Inj1
(
setsum
X7
X4
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X6
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj0
∅
)
)
)
X4
)
)
X7
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
Y
)
)
W
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
)
)
)
)
(
Inj1
(
setsum
Y
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X4
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
Y
)
)
)
)
X5
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X6
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
(
Inj0
∅
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X5
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X4
)
)
X7
)
)
X5
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
X7
)
)
Z
)
)
X5
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
Z
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
X7
)
)
X6
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
Z
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
X4
)
)
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X5
)
)
X4
)
)
X7
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
Y
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X6
)
)
X5
)
)
X
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
50ced7...
and proposition id is
469356...
Proof:
The rest of this subproof is missing.
∎
Theorem.
(
conj_CombUnif_TMJA4pDiUVjc3EqLXMJTz4Q5bMK2m5kZ77v
)
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X7
)
)
X4
)
)
X4
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
X4
)
)
)
)
(
Inj1
(
setsum
Z
(
Inj0
∅
)
)
)
)
)
)
)
X6
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
∅
)
)
)
(
Inj0
∅
)
)
)
)
)
Y
)
)
)
)
)
)
W
)
)
X4
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X5
)
)
X6
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
Y
)
)
Z
)
)
Y
)
)
X6
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
X5
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj0
∅
)
)
)
X
)
)
)
)
X
)
)
X5
)
)
(
Inj0
∅
)
)
)
X7
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
X4
)
)
X5
)
)
X6
)
)
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
W
X
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
X
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X4
)
)
X4
)
)
Y
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X7
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
(
Inj0
∅
)
)
)
X5
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Z
X6
)
)
X4
)
)
X4
)
)
X6
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
(
Inj1
(
setsum
Z
Y
)
)
)
)
X5
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
X
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Z
)
)
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X6
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X6
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
X6
(
Inj1
(
setsum
W
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj1
(
setsum
X6
Z
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
W
)
)
X
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj1
(
setsum
X5
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
∅
)
)
)
Y
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
(
Inj0
∅
)
)
)
X4
)
)
X4
)
)
)
)
)
)
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
X5
)
)
X7
)
)
X5
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X5
)
)
)
)
Y
)
)
X5
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
X7
)
)
Y
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj0
∅
)
X4
)
)
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
∅
)
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X7
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X6
)
)
X4
)
)
X4
)
)
X7
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
W
Z
)
)
(
Inj0
∅
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X4
)
)
)
)
)
)
(
Inj1
(
setsum
X4
(
Inj1
(
setsum
X7
X5
)
)
)
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
X5
Z
)
)
W
)
)
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
X7
)
)
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
X
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj0
∅
)
Y
)
)
)
)
)
)
(
Inj0
∅
)
)
)
)
)
)
)
)
)
→
(
∀X4 :
set
,
combinator
X4
→
(
∀X5 :
set
,
combinator
X5
→
(
∀X6 :
set
,
combinator
X6
→
(
∀X7 :
set
,
combinator
X7
→
combinator_equiv
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X4
)
)
X4
)
)
X7
)
)
X4
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
Y
(
Inj0
(
𝒫
∅
)
)
)
)
X
)
)
X7
)
)
W
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
W
)
)
X6
)
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X
X
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
W
)
)
)
)
(
Inj0
∅
)
)
)
(
Inj1
(
setsum
X5
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj1
(
setsum
X7
X4
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
(
Inj0
∅
)
)
)
X6
)
)
(
Inj1
(
setsum
(
Inj0
∅
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
(
Inj0
∅
)
)
)
)
)
(
Inj1
(
setsum
(
Inj1
(
setsum
(
Inj0
(
𝒫
∅
)
)
Y
)
)
(
Inj0
(
𝒫
∅
)
)
)
)
)
)
)
)
)
)
)
)
→
False
In Proofgold the corresponding term root is
8f7732...
and proposition id is
c20e46...
Proof:
The rest of this subproof is missing.
∎
End of Section
CombUnif