Beginning of Section AIM2_00

Variable X : set

Variable m b s : set → set → set

Variable e : set

Variable K : set → set → set

Variable a : set → set → set → set

Variable T : set → set → set

Variable L R : set → set → set → set

Variable I1 J1 I2 J2 : set → set → set

Hypothesis HL : Loop_with_defs_cex2 X m b s e K a T L R I1 J1 I2 J2

Hypothesis He : e ∈ X

Theorem. (conj_AIM2_TMQWq4bsQFgCcWeDGKLKmozJi8RYaTZenEk)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is ae2a79... and proposition id is 95f254...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMRaPtcK6Tk7ueo8rLTRPjdPFQcYC7ftaWC)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 259f3e... and proposition id is 18f22c...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMPFLCaAkQpRGeRmYVCR23gSnWTAesy9jS8)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (I2 X14 (R X15 X16 (R X14 X15 (I1 X16 (I2 X14 (R X15 X16 (R X14 X15 (I1 X16 (I2 X14 (R X15 X16 (R X14 X15 (I1 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 32dc21... and proposition id is 91181b...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMYa8FLZojmhscBiWY8NUtDNFtLJozjGNzo)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (J2 X15 (R X14 X15 (T X14 (J2 X15 (R X14 X15 (T X14 (J2 X15 (R X14 X15 (T X14 (J2 X15 (R X14 X15 (T X14 (J2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is a83872... and proposition id is eda0cb...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMKP7LuhB1M4em7yZgqdjNWBcCXaVjdC7f)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 05f781... and proposition id is b1012d...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMHi8Hi3e4xFxx5XPNv3UpiQXDAMb968uAk)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 66f4da... and proposition id is 7dd8c3...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJ6xdVJrmMwxAGZk53NSxLJWbAgpFbXSgK)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 3c58a4... and proposition id is 9307ab...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMPUphiL5hkNSYFWNknGjk8TzvVc16CofKg)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I1 X15 (L X14 X15 (I2 X14 (I1 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 6b7b8a... and proposition id is 04fce4...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMYRbf449F7sBaVRZtUcgjb1U4niPb3oHP3)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (J2 X16 (L X14 X15 (T X16 (L X14 X15 (J2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 67c063... and proposition id is 5c8923...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMZdpfqJP3nzdDxPRKeVaFU4KxyWrRxr5pL)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is caf683... and proposition id is 90fefc...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMPYXQBuErdLWq2eRb2o5aHgttanvJPXqJw)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 4d442f... and proposition id is 458fd3...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMXZvsueBnp1uLA5f3VC8KoGBsg6k5wHTYz)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is b2b2f2... and proposition id is 0af97f...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMbyVoHjRKfgtV63S9BBRiyUt5UUSNC2DqV)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is dab2d4... and proposition id is 43bc75...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMLCybfq5zFx1p8oAgstdQPVKL3CgmCB3MF)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is d16c3d... and proposition id is 8e809d...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMLZc5evLdACv9pp755e9DzvhQPT2S8bo7H)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (T X14 (L X15 X16 (R X14 X15 (J2 X16 (T X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 5604a5... and proposition id is 13d02f...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMWRCz9KWAYBE4dqBpxmLntBwsq79Uq2o9K)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (J2 X14 (R X15 X16 (L X14 X15 (T X16 (J2 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (I1 X15 (R X14 X15 (T X14 (I1 X15 (R X14 X15 (T X14 (I1 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 21c539... and proposition id is 5fcf46...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMFEB7dZWXGWHJZYfCMjnUPD1mkEPmeTg6s)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 54f86e... and proposition id is 8b295e...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMEm9F2Hgj4My42PWXBHpCPhoaaWVywHYhK)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is d05a12... and proposition id is be33d8...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMY4T3RfV8GBmpVC7Pc6MCTCXDCXu5RppeY)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (T X15 (R X14 X15 (I1 X14 (T X15 (R X14 X15 (I1 X14 (T X15 (R X14 X15 (I1 X14 (T X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 9da55d... and proposition id is c8d5a0...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMWKeUz6iDxwhWxTetLCdJZGhDSt6hBER8Z)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (I1 X16 (L X14 X15 (I2 X16 (L X14 X15 (I1 X16 (L X14 X15 (I2 X16 (L X14 X15 (I1 X16 (L X14 X15 (I2 X16 (L X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 33ccec... and proposition id is 99f057...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMaQPj85fAZVZxAhpSPoYxithFVGTdE3fnR)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 60aae6... and proposition id is 3b3cde...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMgFT69xijxXRU5fgEjg2wWaeJXQPs9FZk)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (T X14 (L X15 X16 (L X14 X15 (I1 X16 (T X14 (L X15 X16 (L X14 X15 (I1 X16 (T X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is ac8e51... and proposition id is 1f4a47...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMFVDzhZqjXAksSwxMWwdmjugRtWJFrtrJs)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I1 X14 (L X15 X16 (L X14 X15 (T X16 (I1 X14 (L X15 X16 (L X14 X15 (T X16 (I1 X14 (L X15 X16 (L X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 81287d... and proposition id is c458e0...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMFZ5P5zvj2j8TUHcs2etuXYrNQ7cP2ficy)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I1 X14 (L X15 X16 (L X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is d29fa3... and proposition id is ef1473...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMya3TkNvXbzN8jGcVUF8ZKo6BTFHw22M5)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 3a49e7... and proposition id is 9e99df...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJQHvWk5tHnVyim18ycQFY99pB3ZTe6XfU)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 0f5ca3... and proposition id is 7cff3f...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMb1vBc7zmm9rZVGHxVmU894hjWr8yqxZqx)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (T X16 X17)) = T X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 450a9a... and proposition id is 53cfaa...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMNwwQatWUFc9V2eXirm5PojkNhHsNgr5TJ)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 67afba... and proposition id is d14586...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMVEqtDEeiLNyM2Q6TVFaEjhfkkQvoB3eX9)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (J2 X16 (R X14 X15 (I1 X16 (R X14 X15 (J2 X16 (R X14 X15 (I1 X16 (R X14 X15 (J2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (J2 X16 X17)) = I1 X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 3f9ea6... and proposition id is 7c7308...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMNLnss3m9pgdxeTCSAwPu1zwAjJEFs4CUi)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is d3675b... and proposition id is 7e816f...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMYF1gPPR38y3sgYokK54MYrGFfvkonKUUF)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is d3a30b... and proposition id is 6b7d29...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMaqaE1Xcf8LfVsv83Ke8azdLWAdGX97aWk)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is e1b94b... and proposition id is 3e73eb...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMK4WwAzfLVZ9HsCZaLLoxFgQUP9ebxqenh)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I1 X15 (L X14 X15 (I2 X14 (I1 X15 (L X14 X15 (I2 X14 (I1 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is f29f5b... and proposition id is a38230...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMW7mEiWHMJXdd3GRZajbfMAmsmjrm7MbYU)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (L X14 X15 (J2 X16 (R X14 X15 (I1 X16 (L X14 X15 (J2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 430b2e... and proposition id is a2eb98...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMjGzHj6JyyWKqtVjVTirTimCpdiTbqZgt)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is c2a0fc... and proposition id is b64990...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJ5YdPMfJLE4oRrqZjVk6s8qskrtLmCnJB)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 62afd9... and proposition id is 89a11e...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJPEMuxAHVf7TYnsjXjQ1VFomBCnK2Rh4v)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 4efb26... and proposition id is cfa810...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMd1kEKpRcw1Bg8Cy61svqo6BTeVuVtKiB3)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 064453... and proposition id is 641f59...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMRPqL8sBWNtZpRyJmr3xFxdG4bqMvf81Md)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I2 X14 (R X15 X16 (L X14 X15 (I1 X16 (I2 X14 (R X15 X16 (L X14 X15 (I1 X16 (I2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 72c298... and proposition id is 720416...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMdLpVuHUZ7wmreixV2Y5ozVQjUjjhWhgbq)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 (R X14 X15 (I2 X14 (I1 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 86b3b8... and proposition id is 5aff00...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMc9VCzBmpWviSnJrSzQ75hxknWbnSBJdXo)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is df2106... and proposition id is 6906cc...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMQTaYoguAVNBjWtRGfwkdsFKs14iXSdwbB)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 02fb58... and proposition id is 4bf1cc...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMZEEgYxWej199LjLpimWoSTJbYt6RcnGHz)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I1 X16 (R X14 X15 (T X16 (L X14 X15 (I1 X16 (R X14 X15 (T X16 (L X14 X15 (I1 X16 (R X14 X15 (T X16 (L X14 X15 (I1 X16 (R X14 X15 (T X16 (L X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 8d565d... and proposition id is 7f8ab7...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJNdD2JZ7vfpCQG4LyHiXukGKhiq9fd3Zz)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 703bed... and proposition id is 9828f2...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMQ4bcSskmgmPbZbGYiWwsLQqBWsBMW8tMa)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 867a8e... and proposition id is 1e38bd...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMpT2QAZjUAamRxyNQgKibNPLVWZphvcnY)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is ad176f... and proposition id is 63cc39...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMUjhpmqbCfq17NvL36r3X8gohfEVzmR2A4)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is f6cd52... and proposition id is ada36b...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMc7hYvDkGpeFZ5DbrRqPYyHydSxSLA2JGj)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (L X14 X15 (T X16 (L X14 X15 (J2 X16 (L X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (J2 X16 X17)) = I1 X15 (J2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 5bf7d2... and proposition id is 0d09f0...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMK5SQZAiFZqkRLTeQvsc1boEQZ7acfGqhE)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 (L X14 X15 (T X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (T X14 (L X15 X16 (R X14 X15 (I1 X16 (T X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 22935c... and proposition id is b89131...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMLwofVHi5ZzxxNG8GtAoDVd7L9TiARtGuU)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 (L X14 X15 (I1 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 92cb28... and proposition id is 809f2e...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMRdfYgVU4r1WdUwh1eakv7HUhM5vY28Apr)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is e9a433... and proposition id is 46bb45...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMLV4PZrGTXhazg9KNCiLGGpmsT7gB1bpCD)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is ad04cf... and proposition id is 504873...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMTpejdbfcvU5RuSaHKMorgRiVizochxjYV)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (I1 X16 (R X14 X15 (I1 X16 (R X14 X15 (I1 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 122753... and proposition id is 2801a9...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMVT7rx39hB98WheYa7aJLwqmL5HYrrsDqz)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 (L X14 X15 (J2 X16 (I1 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 (R X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 0b3c55... and proposition id is 60cd65...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMEoGFXbK1sgjNPProh9TeP1dE2kU49Qh8K)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (J2 X14 (R X15 X16 (R X14 X15 (I1 X16 (J2 X14 (R X15 X16 (R X14 X15 (I1 X16 (J2 X14 (R X15 X16 (R X14 X15 (I1 X16 (J2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is e4a987... and proposition id is 3f6312...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMWnKsDjyn9DEoqTtkJyeXrpaPpdU4nV2Pi)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (I2 X15 (L X14 X15 (J2 X14 (I2 X15 (L X14 X15 (J2 X14 (I2 X15 (L X14 X15 (J2 X14 (I2 X15 (L X14 X15 (J2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 (R X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (T X18 X19))) = T X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 78ee3e... and proposition id is 5a8f31...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMmjzycaDcJDcCxemtKPtrg4YWJkFhCNbX)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 14c353... and proposition id is a134a6...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJrQzx7x9eSELsu7fURPM9XQzwFr4y5frC)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is b7b2c4... and proposition id is 3ec874...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMZc4X327RRQiqnC7jVoRF6j4GKFhPBjYrR)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 060b64... and proposition id is 169794...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMVmW8xoa15TYddVKBwxWB7LckHsjp4yZ9g)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 8379ca... and proposition id is cb6d7e...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMFT6EtPH1FVZSQbyrYMpkxeGQXhk7tLSvp)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 7d17ef... and proposition id is 9420d0...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMTqERf8eZmJXLweyjuTSWFxXpcJeJwZqqe)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I1 X14 (L X15 X16 (R X14 X15 (T X16 (I1 X14 (L X15 X16 (R X14 X15 (T X16 (I1 X14 (L X15 X16 (R X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is c4a9cd... and proposition id is 3df9e8...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMF9koU56KBUcCfqgjAdSFZeqVBwaVBUGDd)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 53ee76... and proposition id is 383eae...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMKX1sE9vDZxJxJM42v4gzGbgit5Wm8UemZ)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 6aa52e... and proposition id is ea6128...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMV9LZAHRU1mvqSFMFpF2zahKcRJwdL3Wjm)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 (R X14 X15 (I2 X16 (I1 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I1 X14 (R X15 X16 (L X14 X15 (I2 X16 (I1 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 8ef18d... and proposition id is d74c25...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMQrHecoQdUzt3hvZED6oUBmtJUCYHzrWgp)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is fe331a... and proposition id is ed3d80...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMbpPgjebJcEnzgFEor9vvVQZMhmq2cXfVN)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (T X14 (L X15 X16 (L X14 X15 (T X16 (T X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (T X18 X19))) = T X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 384f91... and proposition id is c18d11...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMYR2WaaxBPwr1zYxZWNKgGVuewGhaBcLhL)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 9c3298... and proposition id is 1fdc33...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMRvSN9r4NVT1uNFeFn1oLspYzsSuyKFAg5)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I1 X15 (R X14 X15 (I1 X14 (I1 X15 (R X14 X15 (I1 X14 (I1 X15 (R X14 X15 (I1 X14 (I1 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 5eb3f9... and proposition id is d56aae...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMUbZ5Fo1N2an7KTWNiAUUV8ifKKrtHCXmw)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 359f3a... and proposition id is e567ee...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMVm7vaehfgFsLvfL4HeJ6S3ga1Q5rxTAda)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 (L X14 X15 (I2 X16 (R X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (L X14 X15 (T X16 (R X14 X15 (I1 X16 (L X14 X15 (T X16 (R X14 X15 (I1 X16 (L X14 X15 (T X16 (R X14 X15 (I1 X16 (L X14 X15 (T X16 (R X14 X15 (I1 X16 (L X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (J2 X16 (J2 X17 X18)) = J2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is b0bd22... and proposition id is b05edf...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMdQNXApLLdf9UytLDYhrX4i12rh5DeJDrF)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is e14396... and proposition id is 29cf65...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMGPdkSwYWeunRHRw3SXT9QDixqJ8LGJ6hQ)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (L X15 X16 (R X14 X15 (T X16 (I2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (J2 X14 (L X15 X16 (R X14 X15 (I2 X16 (J2 X14 (L X15 X16 (R X14 X15 (I2 X16 (J2 X14 (L X15 X16 (R X14 X15 (I2 X16 (J2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 1689c6... and proposition id is 2465c4...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMRWu7CjVyp8cTUtBSbVVVn3Z7A8xpCsvSz)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I1 X15 (R X14 X15 (I1 X14 (I1 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 80e539... and proposition id is d79155...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMYTrj7Dpr4VyQYnncEy9cvUsLwEDfQ7Qvv)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (J2 X15 (R X14 X15 (T X14 (J2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 2aa248... and proposition id is 1a2e3e...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMK4EwWTExiSoWkZZsncTQyBrjcvMr5xof6)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (T X14 (R X15 X16 (R X14 X15 (I2 X16 (T X14 (R X15 X16 (R X14 X15 (I2 X16 (T X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 826200... and proposition id is a99e5a...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMXESskjk9rAK7hL2gbXTi8o4EbrwSU2TXn)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is c0c109... and proposition id is 9dfd27...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMXPcLeY41mNLVf2B9LCbFSdTFkxZVQs9au)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 (R X14 X15 (I2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 6be2f7... and proposition id is 3d51e5...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMMcreFLNmoCwx29Lx1RSPoWRbCsvCE7cUH)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (J2 X16 (I1 X17 X18)) = J2 X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 120e08... and proposition id is 017457...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMUkv2gHUW6UZK7WXJDmSAVAy7TUig2FjQi)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 (R X14 X15 (T X16 (I1 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I1 X14 (L X15 X16 (L X14 X15 (I1 X16 (I1 X14 (L X15 X16 (L X14 X15 (I1 X16 (I1 X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is bb1c3a... and proposition id is deded1...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMS5gPLmT7ZfA8eVbrN3B4CvPFaaHBwGHAH)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (T X17 X18)) = T X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is 9510a6... and proposition id is 43fad2...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMHPChFYGWVDhN51dwFHHeDEZ9ZHrbvgG5T)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (L X14 X15 (I1 X16 (L X14 X15 (I1 X16 (L X14 X15 (I1 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 (L X14 X15 (I2 X16 (T X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 22ecfb... and proposition id is 88e752...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMTgHW7YcF8pQikGrm4yauCLwoTmAsYhTMn)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 (R X14 X15 (I1 X16 (R X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (I1 X14 (L X15 X16 (R X14 X15 (I1 X16 (I1 X14 (L X15 X16 (R X14 X15 (I1 X16 (I1 X14 (L X15 X16 (R X14 X15 (I1 X16 (I1 X14 (L X15 X16 (R X14 X15 (I1 X16 (I1 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (T X16 X17)) = T X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 85129e... and proposition id is d04b22...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMbUYhwmAegzPLPEQR4HNjRXRdwqGQv8XYn)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is c664d1... and proposition id is ee9c43...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMGRNbkTPH6A7QKNPEghVELGJ6qBoaCxe3s)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 (R X14 X15 (I2 X16 (T X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (J2 X15 (L X14 X15 (I1 X14 (J2 X15 (L X14 X15 (I1 X14 (J2 X15 (L X14 X15 (I1 X14 (J2 X15 (L X14 X15 (I1 X14 (J2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (J2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (L X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 795d7f... and proposition id is 068e34...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMbuwTBjhFEv4BHTf2nPb6o118dX5qVSmsq)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (T X17 X18)) = I2 X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 0d7673... and proposition id is 86e2f2...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMLSdVMyBk3tcFY3RBoaMZYpYtZSQcuB3Mn)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (J2 X19 X20))) = R X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 716530... and proposition id is f7f85a...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMUYXBXkER2ZWS6TmeAmvfud8bfgQFcMmFZ)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (R X14 X15 (I1 X16 (L X14 X15 (J2 X16 (R X14 X15 (I1 X16 (L X14 X15 (J2 X16 (R X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False

In Proofgold the corresponding term root is bb1190... and proposition id is 26aafb...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMdhPBzzHtf2nqRV4hR2g7AYUU95dxAtRhb)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 (L X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 04b696... and proposition id is c99907...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMZoxErccU8ayZiyQq8uyyJspsGJAxwW3Vg)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is af77e1... and proposition id is f3fade...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMFab4mLwYHr3XRkR3dz77waWPqrr7nHj6j)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (I1 X19 X20))) = L X17 X18 (I1 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 7ffb7e... and proposition id is 70123b...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMJTgx8u9ahniJCKSMRTyTjxLJVffou9V5b)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (I1 X16 (L X14 X15 (T X16 (L X14 X15 (I1 X16 (L X14 X15 (T X16 (L X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is cca9ef... and proposition id is 0f333d...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMbhQTE6X3CzJddxLzAWktrfaMWkj2xY9YP)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I2 X16 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is a9ee80... and proposition id is dd660f...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMQnSDas9kfNaHfjrBjjBfT3cfEVZdr5t3M)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (I2 X14 (L X15 X16 (R X14 X15 (I1 X16 (I2 X14 (L X15 X16 (R X14 X15 (I1 X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (R X17 X18 (T X19 X20))) = R X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False

In Proofgold the corresponding term root is 4ce67e... and proposition id is 4e761d...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMTrJG86BYWyEvfwYo1jDWZZj55EAwJxRaX)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (R X14 X15 (T X16 (L X14 X15 (T X16 (R X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (T X16 X17)) = I1 X15 (T X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (T X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (I2 X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (R X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 4140f9... and proposition id is 5b2a9b...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMSAx38N38R87wTX9FK3K6amYANBZn24Hp1)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (I1 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I1 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (R X14 X15 (I2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I1 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (I1 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is e26ce6... and proposition id is 5716b1...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMHzVCvfwteUsHGuHm3iCwha4U7aZdkYB79)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 (R X14 X15 (I2 X16 (L X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 (R X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (T X15 (T X16 X17)) = T X15 (T X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (I2 X15 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (R X14 X15 (J2 X16 (L X17 X18 (T X19 X20))) = L X17 X18 (T X19 (R X14 X15 (J2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False

In Proofgold the corresponding term root is 333931... and proposition id is 9694e2...

Proof:

The rest of this subproof is missing.

∎

Theorem. (conj_AIM2_TMSFJLnRTkyjX3vDNnd5VfgDnvzGQqa24J7)

(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (J2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (I2 X17 (I2 X18 X19))) = I2 X17 (I2 X18 (R X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (I2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (I2 X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, (L X14 X15 (T X16 (L X17 X18 (I2 X19 X20))) = L X17 X18 (I2 X19 (L X14 X15 (T X16 X20))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (R X14 X15 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, ∀X20 ∈ X, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False

In Proofgold the corresponding term root is 9ee49b... and proposition id is 93adce...

Proof:

The rest of this subproof is missing.

∎

End of Section AIM2_00