Beginning of Section AIM2
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLhLbMBHJz1KZHo7iSXwYhib3G6P2vv737)
(∀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, (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 (L X14 X15 (I1 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (L X14 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, (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 (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 (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 (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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMawP6GEBkWTTVJWSGQtvHmhT6tXRfDEnn2)
(∀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 (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 (I1 X17 X18)) = I2 X16 (I1 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 (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 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, ∀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 (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, (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 (J2 X16 (R X17 X18 (I1 X19 X20))) = R 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, (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 (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, (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 (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 (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, (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 (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 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGAyBspoKiitj4sPBCnUiWHW2YK1Kzjc3e)
(∀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, (R X14 X15 (T X14 (I1 X15 (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, (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 (T X16 (I2 X17 X18)) = T 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, (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, (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 (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 (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 (J2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (J2 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, (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 (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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaCd4C1fHc4L18ajfoAQ3LWqnhygyD8a7x)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 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 (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 (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 (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, (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, (J2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀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, (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 (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 (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, (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 (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 (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, (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)))))) → (∀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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTxTrswNTHbGXfonKHi99ue7MbyDF9d38H)
(∀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 (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, (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 (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 (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, (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 (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 (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 (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, ∀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 (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, ∀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 (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 (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 (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 (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, (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 (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 (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, (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMruwiaCwrZq7P26FzYHyfcLbv3h3Yt8xp)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 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 (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 (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 (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 (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 (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, (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 (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 (I1 X16 (T X17 (I1 X18 X19))) = T 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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKk67W5zdCVxW2UYmP3mM6hy1KyfKCBnJy)
(∀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 (T X16 (T X17 X18)) = T X16 (T X17 (R 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 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (J2 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 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I1 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 (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 (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, ∀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, (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, ∀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 (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, (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, (L X14 X15 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYnZJ2MLJVXoQoMj3yL4g76g543K33f9Q5)
(∀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 (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 (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 (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 (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, (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, (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, (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, (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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (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 (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 (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 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNkGWgmUkJbjx1F48DujGJekvhvRPsTor1)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L 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, (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 (I2 X17 X18))) = T X16 (I2 X17 (J2 X14 (I1 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, (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, (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, (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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHF79T8Um9WNaGxsW6KhqJNnC6v3nZKcbJ)
(∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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 (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, (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, (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, (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, ∀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 (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLTSqGJE1neBvLCiucjcYyzLP7FHsNBdH3)
(∀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 X17))))))) = X17)) → (∀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 (R X14 X15 (I2 X16 (T 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 (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 (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, (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, (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, (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 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T 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 (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 (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, (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, (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 (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 (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 (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, (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 (L X18 X19 (I1 X20 X21)))) = L 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, (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 (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 (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWoQfNcKNbRutNTqarN548xFh6RcEq9zrL)
(∀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 (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, (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, (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 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (T 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, (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, (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 (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, ∀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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMG1mGBcwk3Fjf2kRwwNRbSRMFCw69mFdkz)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 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 X16))))) = X16)) → (∀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 (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 (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 (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 (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T 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 (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 (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, (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 (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 (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 (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 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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, (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 (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 (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 (I2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXhsQbxRpJEqQwzEmVmdcZK4J67pKxGc1P)
(∀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 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, (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 (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 (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 (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, (J2 X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFTUm2H9arwSFSDMa8jFszDxs4a9gSpQeW)
(∀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, (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T 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, (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 (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 (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, (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 (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, (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, ∀X19 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (L 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 (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 (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 (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 (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 (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 (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, (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 (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 (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, (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdSRe1DJ1L3LA8dc4vDvGoVxP5zFBiy1cU)
(∀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, (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 (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, (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, (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, (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 (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, (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, (R X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMws1CrrHLMUKRceAoP7oPUxUyhcVDCbVF)
(∀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, (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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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, (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, (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFmfdgQjtn2FmNy3U8nAeDHDxvG6ozxt6r)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))))))) = X17)) → (∀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 (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 (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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I2 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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (J2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbbapdPRqqWXnYXxbVs1KNak6LFFbpw6FV)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 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, (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 (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 (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 (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, (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 (T X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRLDQGGULEbYekfwgxdvyPJUr9ry5pRuhD)
(∀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 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (J2 X14 (J2 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, (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, (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 (T X17 X18))) = I1 X16 (T 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, (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, ∀X20 ∈ X, (L X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMH6Upm6XkftV2AVWz3hPzbTYfrBJphQtGX)
(∀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 (R X14 X15 (I1 X16 (I2 X14 (R X15 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, (J2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (T 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, (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, (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, (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 (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 (I1 X16 (J2 X17 (T X18 X19))) = J2 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 (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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (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, (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 (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 (J2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWUk453cf4t9kfTbaHdjWArSkBfmGX4Qkm)
(∀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, (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 (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 (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, (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, (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, (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, ∀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, (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 (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 (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, ∀X21 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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, (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbGNnxvGLWcVgLy6LoMDSexAz7E7Up3MSa)
(∀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 X16)))))))) = X16)) → (∀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, (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, (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, (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, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUQajZv4fzCDaZYVwzR7rvEBWnQ4A3JqYc)
(∀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, (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, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T 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, (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I1 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 (J2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (J2 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, (L X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L X14 X15 (J2 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 (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 (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 (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 (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, (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMS1bhnGJ1DRicgd1DEhMJp719tuNqvphhd)
(∀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, (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, ∀X17 ∈ X, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (T 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, (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 (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, (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, (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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaMuy5TThhK1cyJKcdtaUQ6qijxiXqJwn9)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (T X15 (R X14 X15 (J2 X14 (T X15 (R X14 X15 (J2 X14 (T X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T 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, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 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 (I1 X17 X18))) = I1 X16 (I1 X17 (T 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, (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 (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, (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, ∀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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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, (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 (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, (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 (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 (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 (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, (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUXP2e5sQjDjFVUhbNrhMfKaZuaCZJaTyD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (T 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 (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, (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 (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 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (T 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, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKnZsTNcJcyDMTdJAasnybFSV752iZe5mJ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 X17))))))) = X17)) → (∀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, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T 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, (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 (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, (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, (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, (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T X17 (T 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 (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, (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (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, (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYYVaApMFTooZ9eGuzCUefqT6WfZTegDrF)
(∀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 (L X14 X15 (I2 X14 (I1 X15 (L X14 X15 (I2 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀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 (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, ∀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 (T X17 X18)) = T X16 (T 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, (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 (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 (I1 X16 (T X17 X18))) = I1 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, ∀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 (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, ∀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, (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, (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, (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaUN3iEUQtXHhJjgJ78HrgBibZ88CrLcAE)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 X16)))))))))))))) = X16)) → (∀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, (I1 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (I1 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 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 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, (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 (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 (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, (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 (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 (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 (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, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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, (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 (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, (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMamMiSMtbxb2mSPwcF86JUy8dLanQL9dNi)
(∀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 (R X14 X15 (T X16 (R 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 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, (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, (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 (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, (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 (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, (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, ∀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, (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 (J2 X19 X20))) = R X17 X18 (J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXQRuKv1pbu9J9F9vWM24QP6kkFPvQ5Sfi)
(∀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 X17))))))))))))))) = X17)) → (∀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 (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, ∀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, (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, (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 (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 (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 (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, ∀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 (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 (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, (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 (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, (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 (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 (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, (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 (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 (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 (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLtbc27K9JjbufPGscGYurHP8QcrmTZVyQ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R 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, (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 (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, (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, (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 (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 (J2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (J2 X16 X19))))) → (∀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, ∀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 (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZuMe6VVs7bEyGyJXGFjH3W6RqZ7qcsF1u)
(∀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, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 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, (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 (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, (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 (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 (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, (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, (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, (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 (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, (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, ∀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 (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, (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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, (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXeov9CnzWVQ4vLG9foxHMAR5GV3JAtvqq)
(∀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 (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T 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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (T 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, (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 (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, ∀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 (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 (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 (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 (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, (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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLGD52u1fKRSJLNgNpspPiXqp5QfqfnSQr)
(∀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 (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 (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 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (T 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, (I1 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (J2 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, ∀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 (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 (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 (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, ∀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 (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRrLMkbAKm1F97tFxccom9pojVjysDjdsy)
(∀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, (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 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I2 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, (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 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (I1 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, (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 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (J2 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, (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, (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 (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 (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 (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 (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, (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, (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 (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF2eZ8yp2assDuyqeyispdKEmZLhFnju1h)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (J2 X14 (L X15 X16 (L X14 X15 (J2 X16 (J2 X14 (L X15 X16 X17))))))) = X17)) → (∀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 X16)))))))) = X16)) → (∀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 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (J2 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 (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 (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 (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 (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, ∀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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSv4ZLtoe2QRbrgaPWEhE7m51Bp8xQ5QU7)
(∀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 (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 (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 (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 (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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T 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 (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, ∀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, (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, ∀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, (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 (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 (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, (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYDVSTcSKvxmV3dUmE4qy86pBUvVQ94rFf)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I1 X14 (L X15 X16 (L X14 X15 (J2 X16 (I1 X14 (L X15 X16 X17))))))) = X17)) → (∀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, (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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 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 (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 (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 (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 (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 (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, ∀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 (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, ∀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 (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 (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 (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, (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJAS1CwuBSxjyvQooCyEW3ymaCUH81aSMr)
(∀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, (T X14 (T X15 (I2 X16 X17)) = T 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 (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 (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 (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, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 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, ∀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 (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 (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, (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, (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWVgkXXSzNUdCSXZ7GjZaR5wXAJ9cVm4Zu)
(∀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, (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, (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 (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, (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 (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 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNv3L6p1s6eknTrvDSb1eciD3nLtMgjvxT)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 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, (T X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (J2 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, (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 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 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, ∀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, (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 (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, (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, (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 (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 (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 (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, (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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSKEL8njfgkL3UrV2YBqwNxPJZrr6TzRDo)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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, (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 (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, (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 (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 (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, (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 (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, ∀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, (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbqXHFxsKk82tAfvJ6TzEdNJkDDdzsmMSD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T 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 (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 (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 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (I2 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 (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, (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, ∀X19 ∈ X, (R X14 X15 (J2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (J2 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, (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 (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, ∀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 (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 (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 (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 (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, (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 (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 (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVm9EZzeQcb7mgtANQkSpAHDQ1RebiLieP)
(∀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, (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 (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 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 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, (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 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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 (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, (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 (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT7Arf8j1NLhBr3CSAqSYC2eeCKC3pgcpE)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀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 (R X14 X15 (I1 X16 (I2 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (T X17 X18)) = I2 X16 (T X17 (L X14 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 (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 (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, (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, (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, (L X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (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 (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 (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 (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, (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, (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, (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 (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 (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 (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 (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 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbJ9GjBvy63HyteNnQ47Z169bgZMXwQark)
(∀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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I2 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 (T X17 X18))) = I2 X16 (T 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 (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, ∀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 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPY16ErrEco3BDH6nfyUxifrEKSY6V5Ren)
(∀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 (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 (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 (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, (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, (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, (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, ∀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 (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 (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 (R X17 X18 (I2 X19 X20))) = R 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 (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 (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 (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, (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTEyGXtwK3SxczztqbkiLdLtFJ6PWP4YYY)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 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 (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, (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, (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, (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 (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 (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, (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 (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, (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 (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 (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 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHozL9SnmsmCwNaFETe8gpc4VyMLjZdVip)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 X15 X16))))) = X16)) → (∀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, (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, (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 (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 (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 (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 (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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ3H61PYTbakKvuKtkoHd5gnV5yisa7dL4)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (T X16 (L X14 X15 (I1 X16 (L X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 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, (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, (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 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, (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdRJb3k6H9p3bQTtPhRcGL24kHd1K4rGJu)
(∀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, (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 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, (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 (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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 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, (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWKtWYNLEDYDEhE3UZy2v2rxz3YaFNa4Pj)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T 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 (L X14 X15 (I2 X14 (I2 X15 X16))))))))))) = X16)) → (∀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, (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, (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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T 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, ∀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 (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, (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPeEYeSTnNSB84rrM1KuYXCXuVqcjRQiqB)
(∀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, (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 (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 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 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, (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, (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, (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 (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, (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 (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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, (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMV8jJZfitJ9w1Kgj7N9pu5zzxSCQdVvxrC)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 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, (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, (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, (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 (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, (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, ∀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, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T 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 (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 (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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (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 (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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKnZjddBtPJnPzJZpfgfw6HaB6sFyJmLFP)
(∀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 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (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, (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 (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, (I1 X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 X16 (I1 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, (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, (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, (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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I1 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 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (T 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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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, (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXs84DdWwnxooYzzVXTPjzqgrUiCbvW8qV)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 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 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (R 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, (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 (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, (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 (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, (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, (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVLBNTMHcBLpr1GgsZ769Ks5AXa5hW5cuA)
(∀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 (L X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 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, (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, (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 (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, (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 (I2 X17 X18))) = I2 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 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀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, ∀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 (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 (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 (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 (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, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbnof1xrZJhSGREU6ZAXuhruhkK8uV6cse)
(∀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 X16)))))))) = X16)) → (∀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 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, (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, (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 (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, (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 (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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSkmrcYDU3cHDFoAS3NHFQqNn73dP1TyJk)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 X17))))))) = X17)) → (∀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 (L X14 X15 (I1 X16 (L X14 X15 (I1 X16 (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, (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, (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, (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, (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, (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, (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 (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 (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, (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 (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, (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 (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 (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, (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 (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 (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 (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 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT6sPkXq45sjXEpqDZVq6hGjxWxPYMVD5X)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 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 (I2 X17 X18)) = I2 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 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 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, (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 (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, (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMzg9HCXPWtommbSXXiBACf71zVnDFcyzY)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 X16))))) = X16)) → (∀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 (R X14 X15 (I2 X16 (I1 X14 (R X15 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 (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 (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, (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 (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, (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, (T X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (T 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, (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 (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, (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbxmw7vzosKaZcECL8dDGPsLvo5JxE1FUJ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L 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 (R X14 X15 (T X14 (I1 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, (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, (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 (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 (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 (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, (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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGxd8PLXYSw4y3SbxvbCy3WqSJHkPSa1G7)
(∀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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 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 (I1 X17 X18)) = I2 X16 (I1 X17 (R 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, (I2 X14 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 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, (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 (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, ∀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 (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, (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, (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, ∀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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRnHpYkay4nnUE4aAQF9wCBa6J1aGeU3Hx)
(∀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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 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, (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 (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 (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, ∀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 (T X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (L X14 X15 (T X16 X19))))) → (∀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, (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 (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, (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, (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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMax26TXWAJehyMywQ6iTerjvohncbXBSc1)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))) = X17)) → (∀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, (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, (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 (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 (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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 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, ∀X19 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (T X18 X19))) = J2 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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSEqjknQ7XzkURKgZGoKT9j9K1Y1f5ti4L)
(∀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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 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 (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 (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 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (J2 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, (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, (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 (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, (R X14 X15 (J2 X16 (R X17 X18 (J2 X19 X20))) = R 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 (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 (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, (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaGQ95gfbW4twf9ZH5rSfZbsRPyxqA6tVb)
(∀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 (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 (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, (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 (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 (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, (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, ∀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, (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, (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, (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 (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, (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 (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 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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, (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQtnq7VHb42ytXjqom3xuCrLiFVoRTHNNC)
(∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 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 (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 (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 (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 (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 (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 (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, (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, ∀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 (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 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGdCJPrxwjG7BU3rkTRQKiToXRebkERKKz)
(∀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 (I1 X17 X18)) = T X16 (I1 X17 (L 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, (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 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 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 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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 (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, (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, (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, ∀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 (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, (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, (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 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L 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 (I1 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXmVEbmyi7QNdvr3defTCvqKui62SrwUZ1)
(∀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 (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 (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 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (J2 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 (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, ∀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 (T X16 (T X17 (J2 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZNBfs4Q3NpMzfTFxsFqC55fLSK62bDQFc)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T 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 X16)))))))) = X16)) → (∀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 (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 (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, (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 (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 (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, (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, ∀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 (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, (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, (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, (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 (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 (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 (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 (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, (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 (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 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXpZUhCLtd8qfaJVYbdcLWTjuKas8G9EHK)
(∀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 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (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, (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 (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 (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, (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 (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, (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, (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 (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, (L X14 X15 (T X16 (I2 X17 (J2 X18 X19))) = I2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMK9xN1BGVkW1JJfPP167RXZj8YAFuVy6dr)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I1 X14 (R X15 X16 (L X14 X15 (T X16 (I1 X14 (R X15 X16 (L X14 X15 (T X16 (I1 X14 (R X15 X16 (L X14 X15 (T X16 (I1 X14 (R X15 X16 (L X14 X15 (T X16 (I1 X14 (R X15 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, (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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 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, (J2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 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, (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, ∀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 (J2 X16 (R X17 X18 (I1 X19 X20))) = R 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 (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 (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 (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 (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 (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, (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMG3YGNuai7JrTzG1c2pRe7TzYeA2S8xFx2)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (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 X17))))))))))))))))))) = X17)) → (∀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 X16))))))))))) = X16)) → (∀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 (J2 X17 X18)) = T X16 (J2 X17 (R 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, (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, (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, (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, (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, (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 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T 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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbAPgcU2QMntqMPkycXhggBtkcQZ7ZKpY8)
(∀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, (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, (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (T 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, (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, (T X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T 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 (J2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRVgTB9RuQHXppzfisFksYxQtjW5ka22YY)
(∀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, (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, (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, (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, (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 (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGKioAh7gpHnEhQvNzFnyGjsP16BZ1zdKH)
(∀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 (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 (J2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (J2 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 (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 (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 (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, ∀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, (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, (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 (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, ∀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, (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 (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 (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, (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 (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, (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 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPjTKsD5rcef21eY5KF461TiYa1rHZddVw)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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, (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, (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, (J2 X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (J2 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 (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, ∀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 (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 (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 (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 (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, (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTnbtqWL4qZuokMEf9NxXN87mPitgTNMYn)
(∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (J2 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, (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 (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, (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, (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 (T X16 (I1 X17 (T X18 X19))) = I1 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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKzdKoPTc8gbur7kBGTUTQwceYTQCiv48V)
(∀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 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, (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 (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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = L 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 (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 (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, (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZDqYZrMa38Tho94LYfxeqgxbnagYoZ2GL)
(∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (R X14 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, (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, (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, (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 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (T 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, (L X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 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 (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, (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, ∀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 (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 (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 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHZ6f8nRdnnAt1DGqR22e28SrgAYGv3oCA)
(∀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, (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, (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, (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, (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, (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 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQkTovoZsP6GiJSCuVasZfo7LTBNgTsSJG)
(∀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 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (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, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 X16))))) = X16)) → (∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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, (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, (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 (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, ∀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 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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, (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 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWVWX3TL2d3Ufiu8wQHjvXCKTcKQ77c6cK)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 X16)))))))) = X16)) → (∀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, (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, (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 (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (L X14 X15 (J2 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPaRhzCsETgHMNFgam4voRKKXGEgxzvhug)
(∀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, (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 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, (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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (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, (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMct87Gg4BofGu5GAhs7Rg3E8mTWD2a4ayf)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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, (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, (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 (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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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, (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 (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, (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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMV8C9ctD4cKy64X6q1zzzF6T8y4PRqnTbW)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16)))))))) = X16)) → (∀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, (I1 X14 (T X15 (I2 X16 X17)) = T 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, (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, (I1 X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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, (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, (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 (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, (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, (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 (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 (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 (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, (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 (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, (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMa1H8YvWsE9m7K9C7R7GsAhd3HATcmgxvG)
(∀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 (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 (J2 X16 (T X17 X18))) = J2 X16 (T 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, (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, (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 (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, (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, ∀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, (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 (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 (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, (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (T X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTd7oDdVKoWJkUTUfF9eGgvyVgPGqC6rUx)
(∀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, (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 (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 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 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 (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, (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, (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 (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, (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, ∀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, (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 (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 (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 (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, (L X14 X15 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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, (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 (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, (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNR1XGHk9atgxyreXRknu2xFBHRHwUzagn)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 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, (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 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 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, (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 (T X16 (I2 X17 X18))) = T 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 (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, (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, ∀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, (L X14 X15 (J2 X16 (R X17 X18 (I1 X19 X20))) = R 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, (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTCeGf3gwKqXEt86Qe1BecBMK1N1rHuXW8)
(∀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, (R X14 X15 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 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, (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, (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 (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, (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, ∀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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ11gYeHtorbzDAFSdnhCdzDoSX8VxQuLw)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T 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 (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 (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, (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 (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 (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, (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, (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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (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 (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 (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, (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, (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRkFPEtGx7yR6j844NQWvCkoJZEdHMyYsY)
(∀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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 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, (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, (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 (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 (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, (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 (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMTsdS7cWCkLNokFkXJEZdFFWDjJZjjYMd)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (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 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, (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 (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, (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 (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, (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 (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, ∀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, (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, (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, (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, (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (J2 X20 X21)))) = R 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, (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNwaPx2ttejmm2yJWAYzgFuSCGurvKJKTu)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T 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, (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 (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 (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, (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, (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, (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFuMuceNAZWLADJrhUyYrgFH7ZpqSWXHuV)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (J2 X14 (R X15 X16 (R X14 X15 (T X16 (J2 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 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, (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, (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 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 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 (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, (J2 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I1 X15 X18))))) → (∀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, (L X14 X15 (T X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L 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 (I2 X19 X20))) = R X17 X18 (I2 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 (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, ∀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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXPoHRfaEGFdsEXiCQQ9DVmMnMdPbstN5S)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (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, (I1 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (I1 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, (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 (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 (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, (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 (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 (T X17 (T X18 X19))) = T 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 (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, (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQyXBNnBAJx7ybLKcEVTxX9niAZnahm8vo)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 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, (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 (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 (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, (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 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (I1 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, (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUargNduBL13RC7DGbKsRHjKBzCEk3wzhj)
(∀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, (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, (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 (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 (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, (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 (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 (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 (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, ∀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 (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMR3Z1iajAW6XuFJ5Fsbr761aj2qhNxvfzH)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 X17))))))))))) = X17)) → (∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 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 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I2 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, (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 (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, ∀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, (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 (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 (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, ∀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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (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, (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSTwCErzwJ28Tt6Ce9mUMttXbiJ4dJPHXx)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀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, (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (I2 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, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 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 (I1 X16 (T X17 X18))) = I1 X16 (T 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 (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, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T 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 (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 (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 (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 (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 (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 (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, (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, (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTxtmRrTrMaL3PehaKWjhaZ4z4EgXWdrpg)
(∀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 (I1 X17 X18)) = I1 X16 (I1 X17 (L X14 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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 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, (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (T 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, (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 (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 (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 (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 (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, (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 (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 (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, (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGRHSUEc8hegdWsAeoBg8PXCwCSYuPeQhf)
(∀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, (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 (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 (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 (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, (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, (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, ∀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 (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 (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 (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 (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, (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 (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, (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 (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 (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, (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 (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 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdLRoWSfLujs1oqniNe4LR4s3jKCUHG6tf)
(∀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 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (R 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 (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 (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 (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, (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 (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, (R X14 X15 (J2 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (R X14 X15 (J2 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 (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, ∀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 (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 (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, (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, (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, (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMY5TViFFjTsiv6z2sPu7ordmYUeQYUZuV9)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀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 X17))))))))))) = X17)) → (∀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, (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 (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 (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 (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, (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, (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, (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 (J2 X18 X19))) = I1 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 (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 (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 (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 (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, (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 (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, (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcYSUbHgjSpeAstns8dEPmaNPrFpxPA4cq)
(∀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, (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, (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 (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, (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, (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 (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, (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, ∀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 (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 (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 (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 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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, (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 (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 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSkutt8T7dV8X8Xja3ds7ZbVSwsFwFt7uD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (J2 X15 (L X14 X15 (I2 X14 (J2 X15 (L X14 X15 (I2 X14 (J2 X15 (L X14 X15 (I2 X14 (J2 X15 (L X14 X15 (I2 X14 (J2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T 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, (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, (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, (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 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, (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, ∀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 (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 (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 (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, (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, (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 (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 (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, (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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMH1p523wJ63Ca1VtgunjqAkPwCZKWhAnG1)
(∀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 (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 (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 (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 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T 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, ∀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 (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 (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, ∀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)))))) → (∀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)))))) → (∀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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLa2m66WfCx8oCr4MXDs8e5iDjSuM83WHh)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (J2 X14 (R X15 X16 (L X14 X15 (I2 X16 (J2 X14 (R X15 X16 (L X14 X15 (I2 X16 (J2 X14 (R X15 X16 (L X14 X15 (I2 X16 (J2 X14 (R X15 X16 (L X14 X15 (I2 X16 (J2 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀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, (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 (T X17 X18)) = I2 X16 (T X17 (R X14 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = L 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 (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 (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 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJsaGWHf1WxXPGcd1eKegWmhiCDWEiw2ZD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (J2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 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, (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, (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, (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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 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, ∀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 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 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 (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, (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 (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, (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLtMeEqB1nE5HnetPAddTHsxEouaJ3o5j9)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (R X15 X16 (R X14 X15 (J2 X16 (I2 X14 (R X15 X16 (R X14 X15 (J2 X16 (I2 X14 (R X15 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, (I1 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 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 (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 (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 (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 (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, (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, ∀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, (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 (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 (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, ∀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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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, (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 (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, (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 (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 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMEji1q5nfvMxBjNPHCGqYQC1yf8zypqci8)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 (J2 X16 (J2 X17 X18)) = J2 X16 (J2 X17 (L X14 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 (T X17 X18))) = I2 X16 (T 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, (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, (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, ∀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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (R X14 X15 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTKa1sr9rhoBySHMCkD9EB1y8qivEfqZZV)
(∀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 X17))))))) = X17)) → (∀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 X16)))))))) = X16)) → (∀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 (T X17 X18)) = I2 X16 (T X17 (R X14 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, (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 (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, (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 (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, (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (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, (L X14 X15 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMR72sfuesaD2QgBM2VrQS99mx8HNXbpj6T)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16))))) = X16)) → (∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (R X14 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, (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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (I1 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 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (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, ∀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 (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 (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 (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 (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, (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 (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKhDsbL3QL2bPtNTEPVw7GE5nhP9nQE4Tq)
(∀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 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 (R X14 X15 (I1 X16 (I2 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, (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 (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 (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 (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, (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 (I1 X17 X18))) = I1 X16 (I1 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 (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 (T X16 (I1 X17 (T X18 X19))) = I1 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbgPPKra8TvoG8ZJLEpcM4ZFXFd8e6PbBa)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 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 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 (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 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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, (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, (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, ∀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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMP4XjPAcBpcZtzcMaJ1qeo3goiQddrtVB5)
(∀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, (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R 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, (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, (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 (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 (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 (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 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 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 (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, (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 (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, (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 (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 (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 (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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYZge3jH4ofq1k7E1rJ2MYTeqoAzfXAHdD)
(∀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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 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, (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, (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, (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, ∀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, (L X14 X15 (I2 X16 (J2 X17 (J2 X18 X19))) = J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF2uPvyJ6zhM73yzS6VkvrDvmN73UMV1nY)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 (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, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 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, (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 (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, (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, (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, (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTapLPfPJsogYQ4RPWVYuUeLnu7WdmCM9a)
(∀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 (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 (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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (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 (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, (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 (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, (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMc7j7DLuZRhU8kVAPbjmgPBjTpn7wqaNnU)
(∀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 (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 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 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 (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, (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 (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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPFkAf6BaS4h23HCCq5csdxBmVtfHzFxFq)
(∀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 (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, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16))))))))))) = X16)) → (∀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 (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 (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, (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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (T 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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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, (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, (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, (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 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWHatNh7oxN846pkYLYJ4pSVxYPp1vu1Fe)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T 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 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (R 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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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, (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbKQK4JDipzL3iZDMWGQEPgE9TQNFanHLv)
(∀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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀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 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T 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 (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, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T 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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdZA4hbDE2pv1iqqN2nzR5RsDHUyFhvVye)
(∀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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 (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 (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 (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, (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 (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, (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, ∀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, (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 (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 (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, (R X14 X15 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T 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 (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 (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, (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMccuo2PnJWxkk9iHtXVCA7ASfwKKo2Ln4s)
(∀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, (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 (R X14 X15 (I2 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 (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 (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 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (J2 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, (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 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 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 (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 (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 (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 (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, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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)))))) → (∀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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKAU8SeqPseaJuj6293AZNXRhu6G1u9Muj)
(∀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 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀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, ∀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 (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 (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, (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 (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, (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 (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, (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, (L X14 X15 (I1 X16 (J2 X17 (T X18 X19))) = J2 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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMM3JQdmtAvk9Ce1y7VGZVbhQYp5syuXbG2)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T 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, (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, (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 (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 (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 (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, ∀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 (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 (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, (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, ∀X21 ∈ X, (L X14 X15 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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, (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 (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 (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 (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, (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKXPsPauBsf62gdwwAaza3nTJoP7xXWhjk)
(∀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, (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 (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, (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 (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, (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 (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, (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 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 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 (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, (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, (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 (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 (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, (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 (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 (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 (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, (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQgDZiM8ULkqd8Bwv3JXdgFZ8k8uWV18gE)
(∀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, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 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 (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 (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 (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, (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 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 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, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (I1 X16 X19))))) → (∀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, ∀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, (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 (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, (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 (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 (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 (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 (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, (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 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQ9ZbH9TQvFeub7GM8GshGnKc3fdzxYfeM)
(∀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 (I2 X17 X18)) = T X16 (I2 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, (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 (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 (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 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 X14 (I2 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 (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 (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 (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 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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, (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 (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 (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 (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 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRxgVNWVMNNfR6B1HMTb5rjiwNcTMjzR6M)
(∀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 (J2 X17 X18)) = I2 X16 (J2 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 (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 (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, (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, (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 (T X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 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 (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, (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 (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 (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 (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, (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 (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, (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, (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSxfe1LKrFX8Di43bWbaLU6cSsCzJenu2T)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 X16))))))))))) = X16)) → (∀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 X17))))))))))) = X17)) → (∀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, (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 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (J2 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, (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 (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 (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 (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 (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 (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, (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 (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, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVbmbCkb8QSW1d35XC68ctZDGGMwYRnyCv)
(∀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, (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, (J2 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (J2 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, (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 (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 (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, (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, (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, (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 (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 (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, (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 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUVLMbqo1Vw74q1eERot1t2gkC9VnyuCTp)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L 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, (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 (J2 X17 X18))) = I2 X16 (J2 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, (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, (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 (T X16 (I2 X17 X18))) = T 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 (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, (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, (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, (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, ∀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 (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 (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 (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 (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, (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFmMr4H2gsggKrJmjedoxALMYWvj8UUyUU)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (J2 X16 X17)) = I1 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 (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 (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, (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 (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, (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, ∀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 (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, ∀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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVzAkV6nRKJ9C2n1agR2hsCWYtasp7w9hv)
(∀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, (J2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (T 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, (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 (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 (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, ∀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 (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, ∀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 (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 (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 (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, (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 (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 (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, (R X14 X15 (T X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFnz9gQU2r9Fo93EojRsYsanjzCMJC4vzN)
(∀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 (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, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀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, (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 (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 (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 (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 (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 (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, ∀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 (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, ∀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, (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 (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 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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, (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWjUogbwfakqi8qcov6ZqtzBukuKueif5M)
(∀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 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 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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 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, (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, (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, (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRDZChdSRcAb6Wotw6kh9sT4UNds8ik68k)
(∀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 (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 (T X14 (I2 X15 (R X14 X15 (T X14 (I2 X15 X16))))) = X16)) → (∀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, (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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 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, (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, (J2 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 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 (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 (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, ∀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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHfw1NEu6WgMRmVWFEksEYwFTHUQtQH7XZ)
(∀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 (L X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀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, (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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T 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, (I1 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (I1 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, (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNPPqTjqLxU1uXMvoGywuVSmweMPcRksmY)
(∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 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, (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 (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, (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, ∀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, (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 (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, (L X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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, (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXAdJ6eY4v1PSTviB4M5Z6mvnXgRHmyUfh)
(∀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 (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 (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, (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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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, ∀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 (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, ∀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, (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, ∀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 (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 (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 (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, (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFu6DQ9ij4NxoVzP9SLezq3T9sTB5pG5UY)
(∀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, (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, (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 (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 (J2 X17 X18))) = I1 X16 (J2 X17 (T 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, (J2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 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, (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, ∀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, (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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTWmLuCHMTMLhKhEm7NzCDTC7aaMADCJep)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 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, (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, (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 (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (I1 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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMS6iRa4Nfad1NR6Znqm2yqNZswNBecga5M)
(∀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, (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 (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, (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, (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQTv8HcvqbYhasxJyqfMhEKTYoeLXuCoBS)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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 (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 (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, (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 (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, (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, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R X14 X15 (I2 X16 X19))))) → (∀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, ∀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 (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, (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVPdLDEtfqw4cErX2EVkYoy2CkTvgD3owx)
(∀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 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 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, (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 (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 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I2 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, (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 (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, ∀X19 ∈ X, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (L 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 (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 (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, ∀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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (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 (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 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMP1KmTgnvXoH2EkuRGfmDT8m9mjXZDi1rP)
(∀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, (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 (I2 X17 X18))) = I2 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, (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 (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 (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, (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 (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, ∀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 (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 (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 (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 (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 (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, (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUcxx8sZjuDMKpGebXmdz7uAZpmrnKH55a)
(∀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, (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 (L X14 X15 (I1 X16 (I1 X14 (L 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 (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 (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, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 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, (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 (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 (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, (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 (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, (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 (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 (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, (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 (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 (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRzQkFatLXxwMbWFeNDLysSxpqfz2cCxR4)
(∀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 (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 (T X17 X18))) = T X16 (T 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, (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, (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 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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 (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 (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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKgtkq1QG477TXYQDXZP4UDodpWzpyBpRy)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 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 (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, (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, (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 (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, (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, (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, ∀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 (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 (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 (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, (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 (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 (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 (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 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (J2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaJc3EqGzbwruys588yoCf32XzdSvcGoNf)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 X17))))))) = X17)) → (∀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, (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 (J2 X16 (J2 X17 X18)) = J2 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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 (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, (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, ∀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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLDhHexNdGAVPisk3oXBaQDDwZYLwT8Pdp)
(∀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, (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, (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 (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 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 X14 (J2 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 (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 (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 (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, ∀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 (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 (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, (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, (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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, (L X14 X15 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMY6yHLiaSyaEX57aZXjWk3UtwzRp5xvRVq)
(∀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 (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, (L X14 X15 (I1 X16 (J2 X14 (R X15 X16 (L X14 X15 (I1 X16 (J2 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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 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, (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 (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 (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 (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 (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 (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, ∀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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVPbv3tyL97Fq6TzUGaipyaBWoCYuy34Z7)
(∀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 X16))))))))))) = X16)) → (∀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 (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 (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 (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 (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, (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, (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, (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTNPYvq8zxtdHXDW5kyezZ5CViHG86N1Gn)
(∀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 X17))))))) = X17)) → (∀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, ∀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 (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 (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, (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 (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 (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, (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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKPEK8sagDBfDnGUZUFMASicrZ2SSxKwgU)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (J2 X15 (R X14 X15 (I1 X14 (J2 X15 (R X14 X15 (I1 X14 (J2 X15 (R X14 X15 (I1 X14 (J2 X15 (R X14 X15 (I1 X14 (J2 X15 X16)))))))))))))) = X16)) → (∀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, (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 (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, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 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 (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, (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, ∀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, (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, ∀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 (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 (J2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWUiQWzG4ZRAf7BiTY33i9WDyQka45rwtZ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 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 (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 (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, (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 (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, (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, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 X15 X18))))) → (∀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, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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, (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, (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, (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYrKM9iuMbpg4SmdtH5Gwg5wGJJrmG4H1N)
(∀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 (J2 X16 (I1 X17 X18)) = J2 X16 (I1 X17 (L 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, (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 (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, (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 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I1 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, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T 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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcGQUnYpqzjsYJ6fWGkRPzdhedrAedh2g1)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (I1 X14 (R X15 X16 (R X14 X15 (I1 X16 (I1 X14 (R X15 X16 (R X14 X15 (I1 X16 (I1 X14 (R X15 X16 (R X14 X15 (I1 X16 (I1 X14 (R X15 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, (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, (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, (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, (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 (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 (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, (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 (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, (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 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUCEEoncsvMF9D44DHKYxhAA8Z4mZDm5x4)
(∀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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T 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 (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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T X14 (I1 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, (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, (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 (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 (J2 X16 (R X17 X18 (I1 X19 X20))) = R 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 (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 (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, (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJffH2z56LZ1Z5hstiH4wDy9eaCywBdA5b)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀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, (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 (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 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T 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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I2 X15 X18))))) → (∀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, (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 (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, (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, ∀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 (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 (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, (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 (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 (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcR7n7WiUAKib6A9JXCc63AbvTaHJ1yk1v)
(∀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 (R X14 X15 (I1 X16 (R X14 X15 (I2 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 (L X14 X15 (I2 X14 (T X15 X16))))))))))) = X16)) → (∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 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 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 X14 (T 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, (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, (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, (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, (L X14 X15 (J2 X16 (I1 X17 (J2 X18 X19))) = I1 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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L 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 (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, (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKBSXoZFKotgYucKr1R2LRapvAm5tEZhvJ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 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 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (T X16 X17)) = J2 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, (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 (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, (J2 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (T 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, (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, (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, (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, (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 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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, (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFvV7LyxfG6BTzqzDVr9kx7V9vp1xAEAGg)
(∀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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 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 (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (J2 X18 X19))) = I2 X17 (J2 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMX24utqRCDghhyeY1AdzgF2hiELUZcjacx)
(∀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 (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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 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, (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 (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 (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 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (I1 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, (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, (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 (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, ∀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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMc7d6SvE1nUZ69dnYjpHX5YzxAZKNs6gxo)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 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 (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 (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 (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, (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, (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 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, ∀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, (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 (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 (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, (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 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (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 (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 (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, (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPjB9LRPzdzJTMgap4j1dQz5U4m1QQNpDa)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 X17))))))) = X17)) → (∀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 (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 (T X17 X18))) = I2 X16 (T X17 (T X14 (T 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 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T 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 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 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, (L X14 X15 (I1 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 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, (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, ∀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 (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 (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 (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 (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 (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, (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 (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 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKDEE1Qp64HA2UMJKZoWHaGboGUQu2YXHo)
(∀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 X17))))))) = X17)) → (∀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 (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, (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 (I2 X17 X18)) = T X16 (I2 X17 (R 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 (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, (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, (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, (I1 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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 (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, (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 (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, (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 (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 (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF4KfN16J7B5MBkPKXYuRSpt3ZgKpJtkmS)
(∀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, (L X14 X15 (I2 X14 (I1 X15 (L X14 X15 (I2 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 (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 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 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, (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 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 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, ∀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 (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 (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 (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, (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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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, (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 (I1 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQaBtsNbYgoyNpoqonVkvZq3D6BdWPZEKK)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀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 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, (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 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 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, (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 (I1 X17 X18))) = I2 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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMVxNZ9pmkeezA23xLt6ZLEHuLoaHZnnv2)
(∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (R X14 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, (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, (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 (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 (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 (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 (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 (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, (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, ∀X21 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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, (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 (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 (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)))))) → (∀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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbmREhtskgDaaj4FqbEtQrgA79Y9x5ZfJu)
(∀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, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T 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 (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 (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 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (T 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 (I2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVMSfQ7r3zqQvs8VHec1DwNJ9LPK4rQ8xy)
(∀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 X16)))))))) = X16)) → (∀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, (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 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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, (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 (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 (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, ∀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, (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, (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 (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, (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 (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 (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 (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 (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, (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, (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 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQAKvowvG2tDidsRmJEvWmuLLf9dG83yjZ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T X14 (R X15 X16 (L X14 X15 (J2 X16 (T 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 (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 (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, (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, (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 (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, (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 (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, (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 (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, (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKvLr24FvRdu1FCaEZxM1KLFMF2e7o4y8Y)
(∀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, (L X14 X15 (J2 X16 (I1 X17 X18)) = J2 X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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 (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 (T X17 X18))) = I1 X16 (T X17 (I1 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 (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, (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 (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 (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 (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, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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 (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 (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 (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, (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, (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXWQpQkK1me6G8yyUAvPxoF9Hf5J7CYkgc)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 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 (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 (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, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 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, ∀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 (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, ∀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 (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, (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 (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 (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 (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 (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, (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, (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 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZjySg2nj9QrxQ72cbu6PDivLz7yrPz8Vq)
(∀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, (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 (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 (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, (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 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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, (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 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJPHaAvsNXv6QcbkXiUJHmhmuiAoh8Qb2D)
(∀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, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T 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, (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 (T X17 X18))) = T 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, (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, (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, (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 (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 (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 (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, (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, (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, (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 (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 (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 (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 (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 (I1 X20 X21)))) = L 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 (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 (I2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdid9GEMyrfcopCWne1D8fzg5r2fUdarEX)
(∀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 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (R 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, (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 (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, (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 (I1 X16 (T X17 X18))) = I1 X16 (T 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, (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcENRVqaiuL25HCoETuhidEnKcJeRoFC4g)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (T X15 (R 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 (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 (I1 X17 X18))) = J2 X16 (I1 X17 (T X14 (I2 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, (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, (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 (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 (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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, (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTjDhFT1MkREvQBbYQfemWs1WWSzUzf1LK)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T 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 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 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, (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, (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 (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, (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, ∀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, (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 (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 (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, (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 (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, (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMW1WEXhToe94gYNdrqrQDMHovoRmSsguTY)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (T X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 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 (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 (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 (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 (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 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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 (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, ∀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 (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, ∀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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L 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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMExFTnbeGdoJz1sYZvsqi4U1BRw9FVKstb)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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, (J2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T X16 (J2 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, (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 (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 (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 (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, (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, ∀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, (L X14 X15 (J2 X16 (T X17 (I2 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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, (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (T X20 X21)))) = L 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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJtvamKSodDNszDEcr7ELYk6gYBDBsFMWX)
(∀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, (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T X16 (R X14 X15 (J2 X16 (L X14 X15 (T 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 (I1 X17 X18)) = I1 X16 (I1 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, (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 (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 (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, (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 (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, (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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLfNg7sDYLeAViDScn8o46vTPoxBzD662p)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 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, (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 (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 (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 (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, (J2 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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, ∀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 (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 (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, (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, ∀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 (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 (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 (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 (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 (I1 X20 X21)))) = R 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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHC4t5okNhYnhBqUquRBc2DN7YhCJN5aLF)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 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 (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 (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 (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 (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 (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 (I2 X17 X18))) = I2 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 (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 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYiwyZ1coskANKA9oHx8KGELM5WVRaHswq)
(∀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 (T X16 (I2 X14 (L X15 X16 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (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, (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 (T X17 X18)) = T X16 (T X17 (L X14 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, (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, (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, (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTX9YuvQ4B6pSut8Sy8Vk5Erv4HmjjBDjV)
(∀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 (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 (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 (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 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 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 (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 (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, (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXAM2L3kf4qkfuA1kYYgvBP5Mu3Y2aHWVA)
(∀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 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 X16 (L X14 X15 (J2 X16 (T X14 (L X15 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 (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 (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 (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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 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 (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 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 X18 (L 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 (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, (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 (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, (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 (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 (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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (T X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFqiUrNmpD367NgWThV8j7HQ1bRmsQLCmf)
(∀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 (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 (I2 X15 (T X16 X17)) = I2 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, (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, (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, (J2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (I1 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 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀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, (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, (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, (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 (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, (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHkMgJLYVNQNNEtcGc34RcGNJE82VVKh6w)
(∀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, (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 (R X14 X15 (I2 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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (R X14 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 (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, (I2 X14 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (J2 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 (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 (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, (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, (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 (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, ∀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, (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMJigsHu2CgsmqW13YjkU2ockWLTxxspf3)
(∀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, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (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 (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, (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 (I2 X17 X18))) = T X16 (I2 X17 (T X14 (I1 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, (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 (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 (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 (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 (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, ∀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)))))) → (∀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 (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 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMR9zjgZWbdFTXv4p6FvruoHpNk8MpfCuXh)
(∀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 (R X14 X15 (I2 X16 (L X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 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, (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, (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, (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, (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, (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, (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaNuDhHY6dNXd4vYc1Rmz1rpvUYcpLvku6)
(∀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 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 (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 (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 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (T 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, (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 (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 (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 (J2 X16 (I1 X17 (J2 X18 X19))) = I1 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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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 (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 (T X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJRY6Ny4p4YCeMa8rvkDr3fWuUJr1kFMX3)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16))))) = X16)) → (∀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, (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 (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 (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, (T X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T 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, (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNT5CrJGWGa7hoSmnYQ3nouChZSAR99uEW)
(∀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, (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, (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, (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, (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, (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, (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 (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, (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 (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, (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 (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, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGxYfYgvpRBTyL63dyAzwcUkJ7r9mQixL4)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T 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 X17))))))) = X17)) → (∀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, (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, (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, (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 (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, (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 (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 (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, (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, ∀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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMb5LZNSs8ava5M1ZiwhaJBmLb6kqY36o3g)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀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 X17))))))))))) = X17)) → (∀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, (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 (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, (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 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T X14 (T 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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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, (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, ∀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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUvNwez1V9VCw2EDBgRQdPsPE3pAesk2ig)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I2 X14 (R X15 X16 (L X14 X15 (J2 X16 (I2 X14 (R X15 X16 (L X14 X15 (J2 X16 (I2 X14 (R 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 (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 (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, (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 (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, (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 (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, ∀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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTjKbAt3fuq8rBZPX6HoLXZWKqvQD9PzjE)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 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, (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, (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, (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 (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 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (I2 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, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 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 (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, (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 (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 (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 (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, (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 (J2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZKmMZ1JD67JCxLgVcS3wCVDBMffguUSv9)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (T X14 (R X15 X16 (R X14 X15 (T X16 (T X14 (R X15 X16 (R X14 X15 (T X16 (T X14 (R X15 X16 (R X14 X15 (T X16 (T X14 (R X15 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, (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, (I2 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSkDCcKNVs4hRC95qhSN39MC3DemSRKwDd)
(∀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, (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 (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 (T X16 (I2 X17 X18)) = T X16 (I2 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, (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, (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 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (J2 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 (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, (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, (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, (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, (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 (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 (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 (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 (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 (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, (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQM1pJKTKVKbVLv2CyYbU8GDHgLN2AbqBH)
(∀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 (L X14 X15 (J2 X14 (I1 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))) = X17)) → (∀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 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (J2 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 (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 (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 (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, ∀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 (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, (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 (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 (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, (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)))))) → (∀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)))))) → (∀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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNNF33oGxZ2FdQzmpBqCU2gMeBZ45DNMVK)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 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 (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 (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 (I2 X17 X18))) = I1 X16 (I2 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 (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, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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 (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, (L X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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 (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, ∀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 (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 (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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, (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, (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXbEEJPUHnxdEJ43Rpyi1ztvj61JxcXGhp)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀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, (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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 (J2 X16 (I2 X17 X18))) = J2 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, ∀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, (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, ∀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, (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, ∀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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (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, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVQeJxLcDJDFCXszpRHbJcdgEdfuFVHfvh)
(∀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, (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 (J2 X17 X18)) = T X16 (J2 X17 (R X14 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, (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 (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 (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 (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPuMkKxDTawsLJeCLtheKtkT2S8aiDm4z6)
(∀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, (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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, (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, (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, (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, (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 (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, (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 (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, (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, (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 (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 (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, (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 (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 (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, (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (I2 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRhVEwpo3LqrrMHC2mYKxQEB4rH1qC8fFe)
(∀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, (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 (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 (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 (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, (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 (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 (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 (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, (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, (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, ∀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 (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 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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, (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSRrBwU9L2G4nztFC7AKcUP1b29i8TiqtM)
(∀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, (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, (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKJ8Pqqpb8VNxgHd3tvTkbT13zcDHzp65J)
(∀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, (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, (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 (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 (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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (J2 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, (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, ∀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, (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNDgzVT5YtTSsHAU31XpwA9kfjarjnPfZK)
(∀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, (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 (I1 X15 (J2 X16 X17)) = I1 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, (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, (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, (I1 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (J2 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, ∀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 (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, (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, (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 (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, (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, (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 (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 (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 (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 (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 (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbaVtyb32ugvNhDhPpLDbNU8QPispQXtKh)
(∀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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (T 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, (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 (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, (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, (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, (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, (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 (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, (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, (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 (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 (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 (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 (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 (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 (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, (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, (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 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMU8tWU4H8frbSb2d6GcS5idAxWaBYcinf1)
(∀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 (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 (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 (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 (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, (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, (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, ∀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 (I1 X16 (T X17 (I1 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUNEiyK9AHEfHRYsmqCeTGqc6A6opLRkBu)
(∀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 (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I2 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, (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 (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 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (T 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 (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 (J2 X19 X20))) = L 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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLDyUdeecakDBHBQMSuH5i71VPCXDBQqCa)
(∀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 (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, (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 (J2 X16 (I1 X17 X18)) = J2 X16 (I1 X17 (R X14 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, (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, (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 (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 (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, ∀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 (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, ∀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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF4EJ5weC4naYmT2nt8e3r2JHCnEEdDUGd)
(∀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, (L X14 X15 (T X16 (T X14 (L X15 X16 (L X14 X15 (T X16 (T X14 (L X15 X16 (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, (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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 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, (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, (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, (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 (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, (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, (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, (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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, (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVGMBfMnA3vtcArb9jVtziVxBPFa3ifsEU)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T 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, (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 (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, (J2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (T 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, (I1 X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (T 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, ∀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 (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 (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 (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, (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, (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 (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, (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHuGPq2MVay8BqS4xC9fw5mBrFC3HFiLPV)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (L X14 X15 (I1 X14 (T X15 (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 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 X17))))))))))) = X17)) → (∀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, (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 (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 (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, (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 (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, (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, ∀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 (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, ∀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, (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 (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, (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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, (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMP3R9PDfm2BmM8nyLXRekHYwbooBrp88W7)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (I2 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 (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 (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 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdRABWYgUG7rHZjPQt6NSFvp669g8Q7dU8)
(∀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, (J2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 X16 (J2 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, (T X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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, (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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (T 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, (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 (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 (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, ∀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 (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, (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 (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 (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, (R X14 X15 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSKAJrcmuXMse6TnFfyf2Bvh5TTM682Ume)
(∀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, (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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (J2 X16 X17)) = T X15 (J2 X16 (I1 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, (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 (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 (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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (T X14 (I2 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 (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, (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 (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, ∀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 (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMd8AZZHm3s61JB6eS4AfeSjx72GmxuoQMx)
(∀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 X16))))))))))) = X16)) → (∀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 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, (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, (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 (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 (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 (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 (I1 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 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, (R X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 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 (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, (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, ∀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, (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 (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 (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, (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 (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, (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 (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdR1at9CbKpdGHCjAPAcPro3ARv4VQhdwm)
(∀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, (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 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, (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, (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, (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 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, (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, ∀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, (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, (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ8X51jdcgkDoyCMiHdbVnt37SoerpXtZq)
(∀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 (L X14 X15 (I2 X16 (L X14 X15 (I1 X16 X17))))))))))))))))))) = X17)) → (∀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 X17))))))))))) = X17)) → (∀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, (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 (T X17 X18))) = I1 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 (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, (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 (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, ∀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, (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 (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, (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, ∀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)))))) → (∀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 (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXavpwFVWEE5kevsXxrKM4nVFJSF2Wc1cU)
(∀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 (L X14 X15 (I2 X14 (I1 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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 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 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 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 (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 (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, (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 (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 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaTBevZfhHpGYqnMQUpScvXXC3JuW6HSzH)
(∀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, (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, ∀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 (I2 X17 X18)) = I2 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (J2 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, (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 (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, (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, ∀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, (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 (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, (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 (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 (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, (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, (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, (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 (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 (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 (T X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQkC8KhGzEt5tbU9d5MFehb87MUbhM7XWq)
(∀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, (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, (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 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (J2 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, ∀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 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L 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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHahfqUo21A12Qt2NLtoGvt5WBevx3aV5n)
(∀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 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, (T X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 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, (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 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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, (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, (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 (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 (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, ∀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 (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, (L X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQXVsrJp8BRNdWLZF3zqbT9NNF6kWGSAd8)
(∀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, (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R 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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 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, (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 (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, (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 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (T X18 X19))) = J2 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 (J2 X17 (T X18 X19))) = J2 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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNUN43Y4tQLwgTyf3h8uXd1gAVFtc2dcon)
(∀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 X17))))))))))) = X17)) → (∀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 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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I2 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 (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 (T X16 (T X17 X18))) = T X16 (T X17 (I1 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, ∀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, (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, ∀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, (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, ∀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 (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 (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, (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)))))) → (∀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, (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWPNLr54psL3U2aSZGqt9rE9xRPnxPKgkM)
(∀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, (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, (I1 X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 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, (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, (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, (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, ∀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, (R X14 X15 (I1 X16 (J2 X17 (T X18 X19))) = J2 X17 (T 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 (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 (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, ∀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 (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, (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 (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYr8XvECWZcWrZ3RzV98SH8X273moBF5eF)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))) = X17)) → (∀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, (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 (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 (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, (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 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 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, (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, ∀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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJFsGgW13KeEWkoTgaoDPWoFgt7fy3RGxM)
(∀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 (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, (L X14 X15 (I2 X16 (I1 X14 (R X15 X16 (L X14 X15 (I2 X16 (I1 X14 (R X15 X16 (L X14 X15 (I2 X16 (I1 X14 (R X15 X16 (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 (T X16 X17)) = T X15 (T 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 (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 (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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (T 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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGPjJgLEsM4eQXjUwVMWza9pJBGPd7ncSZ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16))))) = X16)) → (∀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, (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 (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 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 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, (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 (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, ∀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 (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 (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, (L X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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 (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 (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRWugZMxFiNbSZ33uh29FFXQZnxdPNaVXd)
(∀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, (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 (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, (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, (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 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T 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, ∀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, (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 (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMN5a29RCNqy3uN1vt8KV4b2VVJzEi85QPH)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 X17))))))) = X17)) → (∀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 (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 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 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 (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, (T X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (J2 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, ∀X19 ∈ X, (R X14 X15 (J2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (R X14 X15 (J2 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 (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, (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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, (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcTXnjLCYyV32BFTrQvi2UEJVfAQoq2Aw8)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 (R X14 X15 (J2 X14 (I2 X15 X16))))))))))) = X16)) → (∀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 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 (J2 X17 X18)) = T X16 (J2 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 (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, (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, (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 (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, ∀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 (I1 X18 X19))) = J2 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 (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, (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (J2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcbxhQGAsqhAB94xwobmrnXBC4Wm88woaM)
(∀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 (T X17 X18)) = T X16 (T X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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, (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, (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 (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, ∀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 (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, (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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKj1obGzzHotqD4MZJkbswFCb1dUKKe6GD)
(∀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, ∀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 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, (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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (T 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 (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 (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, (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWwV4efHFi2LLv9QKgUL9ud8qqhkv4oxYN)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R 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, (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 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 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, (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 (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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 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 (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 (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, (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, (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, (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 (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 (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 (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, (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTbwVQp318gAGAJCrUiPdnsqjWJWJuxG6q)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T 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 (I1 X16 (T X17 X18)) = I1 X16 (T X17 (L X14 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, (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 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (T 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, (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 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 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 (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, (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZZysXyUBiCb6KbV9GM7Ntk6ndaSQZV1NY)
(∀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, (I2 X14 (I1 X15 (I1 X16 X17)) = I1 X15 (I1 X16 (I2 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 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (T 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, (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (I1 X14 (I2 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, ∀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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcsss9puPppjYcefvqV2S2gqqGuRQYJ1fN)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 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 (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 (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 (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 (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 (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 (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, (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, (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, ∀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 (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 (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 (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, (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)))))) → (∀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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXardi9CRDaqSejfaR5u7vR4AjS81KWJH3)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 X16 (L X14 X15 (I1 X16 (I2 X14 (L X15 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 (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 (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 (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, (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, (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 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 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, ∀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, (L X14 X15 (I1 X16 (J2 X17 (T X18 X19))) = J2 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 (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, (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, (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 (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 (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 (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 (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, (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 (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 (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 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMEkLiKECR36gW3jcc6xn5F8Lw7ECStV5Q8)
(∀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, (R X14 X15 (T X16 (I2 X14 (L X15 X16 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (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, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T 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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (T 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, (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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYk169PtdzCsN5ptyuWWDjLXhmAZh5Bby2)
(∀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, (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 (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, (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, (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, (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, (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, (L X14 X15 (T X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (L X14 X15 (T X16 X19))))) → (∀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, ∀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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcV19AHzjnh7ebvpXjipoWQ4auLn4LmczZ)
(∀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, (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T 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 (I1 X17 X18)) = I2 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 (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 (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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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)))))) → (∀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 (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 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcDneuC9eVLkCf1n88z2UFvQy6JuHX62UN)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (J2 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 (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, (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, ∀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 (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, (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, (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 (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, (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 (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 (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 (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 (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, (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 (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXSByjWaAYPCvTavWaMsGHVEj5RTgAMmzr)
(∀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 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (R 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, (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, (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, (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 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (J2 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, (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 (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, (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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, (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 (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 (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 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJQwyin7GCddvXeTaSmb79f9q1tPyrMn2C)
(∀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, (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 (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 (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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (T 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, (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, (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, (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, ∀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 (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, (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, (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 (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 (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, (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 (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXx51qD1BThqquHLZVQt6TEzy5jizXjo9h)
(∀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 (I2 X17 X18)) = T X16 (I2 X17 (L 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, (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, (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, (J2 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 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, (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, (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 (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 (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, ∀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, (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdzhakC3WYn1dDtf1DGz2fFd8dka7m191t)
(∀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 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 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 (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 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 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, (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 (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, (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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (T X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLiccp4yHBKZBatVWLN3myfZFXxHMJLCsD)
(∀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 (R X14 X15 (T X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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, (T X14 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 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, (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, (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, (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, (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 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TML5rks86JULmh7zS44CQDpoBzrwHpxeA2t)
(∀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 (T X17 X18)) = I2 X16 (T X17 (R 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, (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, (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, (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 (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, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTiNXCrTRYmGa2yBx4vvk1q14pNX2nuZXB)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 X16 (I1 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 (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, (J2 X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (T 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, (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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 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, (R X14 X15 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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, (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 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNe5WrtFR4rC7xYVvj4A6astnHpgTr8pC2)
(∀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 (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 (I2 X17 X18))) = T 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, (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, (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, (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, ∀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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (I1 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYJNAXoiRVCZDizPt6M3aPtwukLe2uVE7h)
(∀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, ∀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 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (L 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, (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, (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 (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, ∀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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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, (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaA1UNJH6t1Hydmf2WMNzun1BvEqyHdMrm)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16)))))))))))))) = X16)) → (∀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, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T 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, (T X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (J2 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 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (J2 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, (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, (L X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 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 (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, (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 (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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMaeHMV9CMgbCgY6TE7NUph53DMQjEoBhX)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (L X14 X15 (I2 X14 (I1 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 (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 (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 (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, (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, (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, (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 (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 (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, (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWWYPKV9X8T9jcDWrGTWPopnjmksfKGezK)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (J2 X14 (R X15 X16 (R X14 X15 (J2 X16 (J2 X14 (R X15 X16 (R X14 X15 (J2 X16 (J2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 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, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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, (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (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, (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, (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcafy7Adq1cbCJqcf9SQWwY9JUrATLg8s1)
(∀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, (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 (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 (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 (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 (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 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T X15 X18))))) → (∀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, (R X14 X15 (T X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (T 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 (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 (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 (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 (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, (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRaBq6mP4c1rJj6DK62CovUiaMKjAbhTp9)
(∀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 X16))))))))))) = X16)) → (∀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, ∀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, (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 (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, (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, (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, (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, (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, (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, (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 (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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, (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 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMB3TtYCdvx5fKVqn6LHwcbL99v3FWdYrr)
(∀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, (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, (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 (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 (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, (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 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 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 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (J2 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, (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRRUtqsGY7BQM6E23bwMoYwviHfZp98dob)
(∀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 (T X16 (T X17 X18)) = T X16 (T X17 (L X14 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 (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 (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, (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 (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 (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 (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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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, (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 (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, (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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSAvbW3NG7MMkxkrFfmH3g4kin1tsZXxeP)
(∀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 (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 (J2 X16 (J2 X17 X18)) = J2 X16 (J2 X17 (L X14 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, (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 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (T 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, (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 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUd2XAQYTzeFJ4WvEgR9Uxe3gon5AG2df8)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 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, (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, (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 (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 (T X17 X18))) = I2 X16 (T X17 (T 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 (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, ∀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, (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, (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 (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 (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 (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, (L X14 X15 (I2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJQC7xe6SxCRhzMw2rvjyHyiuFnyWr68eQ)
(∀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 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 X16))))) = X16)) → (∀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 (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 (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 (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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 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, ∀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, (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 (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, (L X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (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 (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 (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 (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 (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, (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHF3KXeAaUhpu67KPvaZbqqk7Tgcqz2yut)
(∀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, (R X14 X15 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (R 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 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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, (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, (T X14 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T 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 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (L X14 X15 (J2 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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFBjvTyiAtrGqzaKoyafq7FjK5dA2u9Dg3)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L 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, (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 (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 (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, (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, (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHbxPW4A8tMzyafSF5bxDBfvJRegvmczmA)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 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, (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 (I1 X16 (I1 X17 X18)) = I1 X16 (I1 X17 (R X14 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, (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, (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, (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 (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 (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, (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUCNN5bPJdFxEPtRCpQqHMGPR8DrsQLtwv)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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, (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, (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, (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 (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, (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, (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, (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, (L X14 X15 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 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 (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, ∀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 (I2 X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcFU7bhNEUVajKbQhSHrS7rtaRmhsUedyf)
(∀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 (L X14 X15 (I1 X16 (T X14 (L X15 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, (I1 X14 (I2 X15 (I1 X16 X17)) = I2 X15 (I1 X16 (I1 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, (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, (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 (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 (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 (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, ∀X19 ∈ X, (L X14 X15 (I1 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L 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 (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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, (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNGGDyJD3gtdA62gFjNDkEdgDLMXspGPL1)
(∀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 X16)))))))) = X16)) → (∀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, ∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 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, (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 (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, (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 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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 (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, (L X14 X15 (J2 X16 (T X17 (I2 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSP5ojbeC2XNoVLcNB7bgt6BaTmAoCEXfA)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 X16))))))))))) = X16)) → (∀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, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (T 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, (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 (J2 X17 X18))) = I2 X16 (J2 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, (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, (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, ∀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, (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, ∀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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUeK9tRCjXmKhwfdtPkEG8M51Hxn2VxBht)
(∀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, (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 (R X14 X15 (T 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 (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 (I2 X17 X18))) = J2 X16 (I2 X17 (I1 X14 (I2 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, (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 (I1 X17 X18))) = I2 X16 (I1 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, ∀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 (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ4SacSdf1tBpiMSzGZcXVrdYECZDrXrJe)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀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, ∀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 (J2 X17 X18)) = I2 X16 (J2 X17 (L X14 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, (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, (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 (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 (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, ∀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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXWRK8Zu3W4YrQTyNi5EuafFtMsVPxyzWC)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (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 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 (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 (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 (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, (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 (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 (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 (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, ∀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 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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, (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, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (L X14 X15 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (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 (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, (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMd1mdzMzRsLmrwqdnW46Tda49rKv9vAkKM)
(∀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, (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, (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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 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, (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, (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 (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, (J2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 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, (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, ∀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 (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, ∀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, (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, (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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXehaBhZ8dWeqFz6PRkUdKW1v7GNDdRojx)
(∀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 (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 (T X17 X18))) = I2 X16 (T X17 (T X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I1 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, (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNiWS2cYSavdR7fD3nHxb1PqcQ5bcPEDjw)
(∀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 (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, (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 (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (I1 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcDBmVjvPLEBjHoVha93kbgQfbCJi8Kdzo)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (I1 X15 (L X14 X15 (J2 X14 (I1 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (J2 X16 X17)) = I1 X15 (J2 X16 (T 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 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I2 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 (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, ∀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, (L X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 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 (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, (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJrfXhP4yXkDjkRsBzteaLCxnyLvBJVnuE)
(∀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 (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, (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, (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 (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 (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, (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJPtpNQpG3tpPn4bwHpeRcdXiGR8hcGoNz)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 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, (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, (I2 X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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 (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 (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 (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, (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 (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 (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbHe39T33RRYNxBg2ijU21r8LXErbTRxmx)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀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 (L X14 X15 (I2 X16 (I1 X14 (R 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, (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 (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 (I1 X16 (I2 X17 X18))) = I1 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, (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, (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 (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 (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 (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 (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 (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, (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 (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, (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 (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 (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, (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPE788qBEcWCSCdFQ2cmFNZYJoSLCBFgxf)
(∀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, (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 (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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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, (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 (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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHS5RHBkBCaZENKPpCAFVNZV15tUMUNFcc)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L 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 (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 (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 (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, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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, (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, (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 (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, (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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, (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKezGVBei2xzVSLUsrivF6QkJ46JXcDYKb)
(∀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, (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, (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 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (T 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, (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 (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 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSCXwyZtmJxZqyq7o29uUHhSfBDXHwCYP9)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀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, (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 (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 (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 (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, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (T 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 (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 (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 (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, (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 (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 (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, (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, (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, (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMZiAuVe23PAGUjuwfcqGBDJJGwzm7AWVU)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 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 (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, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, ∀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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 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 (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 (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 (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 (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, (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 (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, (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVmTgrxgFgm4boXtU3TiCuJBbnNtGXdFuB)
(∀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, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T 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, (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, (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 (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 (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, (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKUP9qFkE6MxbkpRtSag8PngXbU17ZgNX2)
(∀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 (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 (R X14 X15 (T X16 (R X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (T 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, (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 (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, (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, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L X14 X15 (J2 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 (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 (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 (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 (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 (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, (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, (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, (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT7KVV5Z1KCLfRrrPESQ3JLSpa8b3fKRj6)
(∀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, (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 (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 (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, (J2 X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (T 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, ∀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 (I2 X18 X19))) = I1 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 (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 (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, ∀X21 ∈ X, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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, (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, (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)))))) → (∀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, (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 (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 (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 (I1 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLdLWY6cTMNXCCmdR89PJpTNnSFg2Z7s3v)
(∀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, (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, (I2 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (T 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, (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, (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, (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, (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, (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, (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 (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, (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHYAyVzDvtmMPgw3pnMSYA37iNyRgxeg3g)
(∀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, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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 (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, (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 (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, (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbJ8PiWwBh9UBL6WymiHt5epv6G9ePdAbU)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (J2 X15 (I2 X16 X17)) = J2 X15 (I2 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, (T X14 (J2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T X14 (J2 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, (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, (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 (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (J2 X18 X19))) = I1 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 (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, (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 (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUTRg6ntE667fMDLXFQAE9rrN3GvgMPS5Z)
(∀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, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16))))) = X16)) → (∀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 (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 (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 (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, (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 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (J2 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 (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 (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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L 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 (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, ∀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 (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 (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 (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 (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 (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, (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPKdxmUiPFERwPv45CDFooG9Xv9qRgUKej)
(∀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, (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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZmW7nPpbsgR6WXXyDXjhZpatCmaUQknkS)
(∀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 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 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, (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 (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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 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, ∀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 (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, ∀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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (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, (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 (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 (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 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNKS81PMfQQw8FpvsUoFXDAmobe3ZMcD7g)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (J2 X14 (L X15 X16 (R X14 X15 (T X16 (J2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 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 (I1 X17 X18)) = T X16 (I1 X17 (R X14 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, (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 (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 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L 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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVuizfSxTnpjDryU5VB7PPrFY62zicXPRk)
(∀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, ∀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 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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I2 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, (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 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, (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 (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, (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, (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 (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 (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, (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 (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 (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 (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 (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, (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 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQQjXrF2g8HXYCEAmG1FkgYTBirBNsNDPq)
(∀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 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 (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 (J2 X17 X18)) = I2 X16 (J2 X17 (L X14 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, (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 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I1 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, (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 (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, (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 (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, (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, ∀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 (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, (R X14 X15 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (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 (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, (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHUiJ1Erh3wH59GxeZYvwDnaH6VNNPUtAU)
(∀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, (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 (T X16 (T X17 X18)) = T X16 (T 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, (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, (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, (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, (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, ∀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, (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, ∀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 (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 (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, (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 (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 (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, (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, (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 (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, (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRBDTZRB1PtcHka7X8JLcAqzBFoqKc96hw)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 (L X14 X15 (J2 X16 (L X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀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, ∀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, (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, (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 (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, (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, (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 (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, ∀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, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSpfjsQa1fJprxiqbBVF4uAQ7j2aNpVsvv)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 X17))))))) = X17)) → (∀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 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 (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 (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 (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, (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 (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, (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, ∀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 (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, (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 (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 (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 (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 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaUqYVpJVUX2RvgbumRV45GvM5oc6bV5x1)
(∀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, (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 (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 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (T 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 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T 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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaVZz7mHu7TDMVDCbMrEVd694MSyrBUSyG)
(∀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 (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, (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, (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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 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, (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 (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, (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, (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, (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, (L X14 X15 (J2 X16 (I1 X17 (J2 X18 X19))) = I1 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 (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 (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 (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, (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 (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 (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 (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 (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZoCjWoRi2ePHqg4GGngRzXSwja35g2eNF)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 X17))))))) = X17)) → (∀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 (I1 X17 X18)) = T 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 (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 (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, (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, (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, (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 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaiAJNA4kGhguRQuVQVmrrbPCZFdq4JdJD)
(∀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, (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, (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 (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 (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, (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 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I2 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, (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUMB713dpTebJZFAkU7q74HXnRwYfcYYRn)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 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 (T X16 (I2 X17 X18)) = T X16 (I2 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 (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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I1 X15 X18))))) → (∀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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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, (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUmQKeuiC7Gv2aRF5TBCebch244jj6tqny)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (J2 X14 (L X15 X16 (R X14 X15 (I1 X16 (J2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I1 X14 (I1 X15 (L X14 X15 (I1 X14 (I1 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 (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 (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, (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 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (J2 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, (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 (T X18 X19))) = I1 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 (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, (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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVcMJ3EeAmHnfWv1x3ruQC3H5DU1dAtVpF)
(∀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 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 (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 (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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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, (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 (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 (I2 X16 (T X17 X18))) = I2 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, ∀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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbAFBQF4JUvYYBiwk2c4rKKtQcgEm5FQvy)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T 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, ∀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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 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 (J2 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGPpj83r79ne9TMfg95C8BV7H7J1jwJwJD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀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 (I1 X17 X18)) = T X16 (I1 X17 (L X14 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 (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 (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, (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 (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, ∀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 (T X16 (I1 X17 (J2 X18 X19))) = I1 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 (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, (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, (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 (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 (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 (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 (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, (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)))))) → (∀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 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUSENVnfvQ136krxqJ69aguQtjsL7y9a9V)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (J2 X14 (L X15 X16 (L X14 X15 (T X16 (J2 X14 (L X15 X16 (L X14 X15 (T X16 (J2 X14 (L X15 X16 (L X14 X15 (T X16 (J2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (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 X17))))))))))))))))))) = X17)) → (∀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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L 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, (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, (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLWoWtfMkoQrPJxPBJqbqBRsLrBGDAt6yN)
(∀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 (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 (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 (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 (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 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 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, ∀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, (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, (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 (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 (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)))))) → (∀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 (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 (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 (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 (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 (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 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ87eG4dMMkKRoTwcoC1JSaWZUeacpUoGC)
(∀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 (T X17 X18)) = I2 X16 (T 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, (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, (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 (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, (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 (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 (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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L 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 (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, ∀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, (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (I1 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJyp77C5zrCwNQCtMJSSW5viqpJd8iYaxj)
(∀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 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 X14 (J2 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, (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 (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 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 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 (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 (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 (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, (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 (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, (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPFKrxgxregtoEjP9sib8Qz77jfjv7ttdq)
(∀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 X16))))))))))) = X16)) → (∀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 (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, (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, (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, (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, (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, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMR1oH1qRCZHYT5NuJTFKUAXM9PjEJhjHFt)
(∀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, (L X14 X15 (I2 X14 (J2 X15 (L X14 X15 (I2 X14 (J2 X15 X16))))) = X16)) → (∀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 (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 (I1 X17 X18))) = I1 X16 (I1 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, (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLXyRxZU2hn8UFQ6fpncvvyz8ByBP6HFWC)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 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 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 X14 (T 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, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 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 (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, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (J2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcwRZdV3p1TXx85sBjEMVeNDtnKBZBU2xs)
(∀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 (I2 X17 X18)) = I2 X16 (I2 X17 (R X14 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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (I1 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, (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 (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 (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (T X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWVEPF8FcUb66d4ZfV6bGtKcLQ5GF7Bwbq)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 (L X14 X15 (T X16 (T X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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 (L X14 X15 (I1 X16 (L X14 X15 (I1 X16 X17))))))))))) = X17)) → (∀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 (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 (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 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (I1 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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 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, ∀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, (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXK3FMnrosSAXaUvGr1C47vUq4FKzMVzgp)
(∀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 X17))))))))))))))) = X17)) → (∀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, (T X14 (T X15 (I1 X16 X17)) = T X15 (I1 X16 (T 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 (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, (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 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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 (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, ∀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 (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 (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 (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, ∀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 (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, (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 (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, (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 (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 (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 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdZ3UpBzfgjTnvfituZC5CDWTCF5d1UabW)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (T 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, (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 (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 (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 (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, (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, (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, (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 (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, (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, (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, (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHf12BUeTLaxEJDAZxUKq6KnihWPHp4q1v)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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, (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 (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 (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 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 (I2 X17 X18))) = I1 X16 (I2 X17 (I2 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, (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, (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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, (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcEph7vf4FqV6SqE386wgCoqpinXNVkUAf)
(∀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 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 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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 (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 (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 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TML3kwmTz3ffFSihfFaSHRyhuqMGHwZqhcz)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (J2 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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 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, (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, (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, (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, ∀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, (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 (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, (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, (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 (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, (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 (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, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdu8teuEkH2DCTTK9Ke3swBi8aLndCUzGq)
(∀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 (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 (J2 X17 X18))) = T 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, (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (T 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, (L X14 X15 (J2 X16 (R X17 X18 (I1 X19 X20))) = R X17 X18 (I1 X19 (L X14 X15 (J2 X16 X20))))) → (∀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, ∀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 (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 (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, (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, (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 (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, (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 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGjnmCSZWp2aL1ASSMb5ktZAofy8U8kCzp)
(∀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, (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 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, (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 (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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 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, (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 (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, (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 (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 (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 (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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTwKDw3XTyBVMdPgr19u1zb6yXjgmaconr)
(∀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, (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 (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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 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 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (T X17 (I2 X18 X19))) = T X17 (I2 X18 (L X14 X15 (J2 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 (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 (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 (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTeUceTpK2TVB6PageAm7VbgbfMUTuQNNn)
(∀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 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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 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, (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, (J2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (I2 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, (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 (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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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, (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)))))) → (∀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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMax5udMaPcqx6oFHt6ypE2crT6rQaJeyHD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))) = X17)) → (∀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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (I1 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXq9wkRz4CcjzJqGsSobk4LxdWgdTcJFrs)
(∀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 (T X16 (T X17 X18)) = T 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, (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 (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 (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 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 X14 (T 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSybA3Bk2mZ86dwnoZJ8eVA86eLhWZbLNp)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 (L X14 X15 (I2 X16 (I2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀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, (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, (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 (T X16 (I2 X17 X18))) = T 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, (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, ∀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, (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 (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 (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 (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 (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, (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 (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, (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, (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 (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 (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 (J2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMG3WbWAaU5YcdWmHbBbTnA7YRpPt1EvR58)
(∀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, (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, (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, (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, (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, (J2 X14 (T X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (T 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, ∀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 (J2 X18 X19))) = I2 X17 (J2 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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKDPdf5gksd1NDrYvoWhbyJdmtkKGRyvvV)
(∀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, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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, (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 (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, (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 (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 (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, (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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, (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 (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZgmE1LGXwrQ1RSrzSwXCfqBPatV7f9psQ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))) = X17)) → (∀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, (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 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 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, (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, (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 (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, ∀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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (I2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQZYo6TwjfppG7Au3b5AvwfSVv5vg2FaqH)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀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 (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 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (J2 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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPxPVL3XTv9kPxneEWRJzkP8rvwUBthxF8)
(∀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, (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 (I2 X15 (T X16 X17)) = I2 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, (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 (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 (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 (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 (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, (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, (L X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T 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 (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 (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 (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 (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 (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, (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPGi3MQ8E8b2DPao1HrdXsF4bn8enRu9tX)
(∀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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 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, (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, (L X14 X15 (I2 X16 (J2 X17 (J2 X18 X19))) = J2 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 (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 (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, ∀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 (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, (R X14 X15 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWUvuz4rSR9FqJDmpYaUSPEhM4PbjSUh98)
(∀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 (R X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 X16))))))))))) = X16)) → (∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I1 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, (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 (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 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 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 (I1 X16 (T X17 (I1 X18 X19))) = T 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 (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 (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKJ2i2fDaeV5w8HEj4keusUQb2EB73XDJd)
(∀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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 X17))))))))))))))) = X17)) → (∀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 (L X14 X15 (J2 X14 (I1 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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 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, (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, (J2 X14 (J2 X15 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (J2 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 (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (T 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdKX2oAYePLepDzR1ZrCBAiCXxe7x7rvGu)
(∀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 (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 X14 (I2 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, (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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUXvHYRsQG4t8BaVHkgRtBHoF91bisSuwR)
(∀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 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))) = X17)) → (∀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 (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, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 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, (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, (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 (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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMd4tfNRmEW1JxhHRVcWQq6BqXVtdfSydJL)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (T X15 (R X14 X15 (I2 X14 (T 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, (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, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 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, (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 (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 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (I1 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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → (∀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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSRphAV3EqQiTtCAZrc2kEzkRznZjfxPgK)
(∀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, (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T 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 (I1 X16 (T X17 X18)) = I1 X16 (T 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 (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, (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 (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, (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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKT2UkPLRVfEi3UZANwPrKGEQNshwtnGum)
(∀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 (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 (T X16 (T X17 X18))) = T X16 (T X17 (T X14 (I1 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, (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, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 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, (L X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 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 (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, (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, (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 (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 (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 (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, (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 (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, (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 (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 (T X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMc8M9UVAS9XmcjpCJVkc72QaSAiCFjLq8a)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 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, (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 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (J2 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, (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, (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 (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, ∀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 (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 (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 (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 (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, (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (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 (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXr7rzeuUaR61Vwiytxj4mzGtp9xqs9jHv)
(∀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 (I1 X17 X18)) = T X16 (I1 X17 (L X14 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, (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, (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 (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, (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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYBvwBs3ZiEEq8PX673V9TKeJoxqW8piNt)
(∀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 (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 (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 (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 (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, (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, (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, (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 (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, (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, (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, (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, (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPdgkSZzUwiLWEb4DPNqvmznJaGfAPk96E)
(∀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, (I1 X14 (J2 X15 (I2 X16 X17)) = J2 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 (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, (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 (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, (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, (T X14 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (T X14 (J2 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, (L X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 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 (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, (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = L 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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMM7fYX4gPrT2hLKnPULe2MJAGmd9csZo4a)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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 (J2 X17 X18)) = I2 X16 (J2 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, (T X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T 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, (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, (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 (J2 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R 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, (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, (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 (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 (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 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (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 (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 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFWtg85cnrVzQxqEGHYyMMDrYPzemZXvN3)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 (L X14 X15 (J2 X16 X17))))))) = X17)) → (∀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 X16))))))))))) = X16)) → (∀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 (I2 X17 X18)) = I2 X16 (I2 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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 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, (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, (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, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (I1 X16 X19))))) → (∀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, ∀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, (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, ∀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 (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 (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMRE5Egbh3tVUyRyFrm8Lpc6A1HoMwF1Gq)
(∀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, (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 (R X14 X15 (T 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 (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 (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 (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, (I1 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, ∀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, (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, (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFnB1DmCMCsCWQjf9z9toXT1n2XHcPasZ7)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))) = X17)) → (∀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 (I1 X17 X18)) = I1 X16 (I1 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, (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 (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 (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, (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, (L X14 X15 (T X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (T 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 (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 (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, ∀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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T 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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFVvURAQmeoRWVjfzVKCkgnkjiZvCCe1v8)
(∀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, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16))))))))))) = X16)) → (∀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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (J2 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, (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, (J2 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (J2 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, (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, (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 (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, (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 (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, (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbswwMXZgGEYUf7PyXvZPHCLfEsCejh5HY)
(∀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 (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 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 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, (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, (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, (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, (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, (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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJiuvCHm3kh6GABzTrv8N2Kwv2xJx6gE5P)
(∀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, (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 (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 (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 (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 (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 (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 (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, (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 (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, (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 (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (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 (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, (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 (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 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUAdFyjK9SqdKYmfijmCGLq3JoSX8CrfMZ)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 (L X14 X15 (I1 X16 (J2 X14 (L X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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 (T X16 (T X17 X18))) = T X16 (T 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, (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, (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, (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, ∀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 (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, (L X14 X15 (J2 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 X19 (L 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 (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 (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 (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 (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, (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 (I1 X20 X21)))) = L 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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTfNrAV4dKxMb1W27gJGhjk5JGPu19YkJi)
(∀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 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 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, (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, (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, (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, (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 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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, ∀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 (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, ∀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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I2 X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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, (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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (J2 X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXcLPBpxSDEaqu9mYsAeJ7oAiWi3AQ3pN1)
(∀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, (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 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I1 X14 (J2 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, (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, (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, (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, ∀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 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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, (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLB3C53mtXG9EhtJ3wqLEtWH9QhM1DMUAM)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (T 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, (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 (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 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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, (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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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, (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLNRbfuvSHMT1tYj1KKRvGViCHGg5KZMCe)
(∀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, (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 (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 (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, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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 (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, ∀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 (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 (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 (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, (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNkrdkNi27owLVjZCr2TRcvymsvM1bKcv5)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 (R X14 X15 (I1 X16 (L X14 X15 (I2 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 (R X14 X15 (I2 X16 (J2 X14 (L X15 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, (I1 X14 (I1 X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 X14 (I1 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, (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, (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, (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, ∀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 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMyyQvgfAf2e967TFV2eTZCpRhmhDKMeaT)
(∀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 X16))))))))))) = X16)) → (∀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 X16))))))))))) = X16)) → (∀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, (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, (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 (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, (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 (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, (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, (R X14 X15 (J2 X16 (T X17 (T X18 X19))) = T X17 (T X18 (R X14 X15 (J2 X16 X19))))) → (∀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, ∀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, (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 (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 (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 (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 (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 (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, (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 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (I1 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHwNFxP39th25qV8WSRcxpvPdonmMP1MKq)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T 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, (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, (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 (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 (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 (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 (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, (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, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFNsxWv4aVgwS7uy95W39vTPHZnAG2vwm7)
(∀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, (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, (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, (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (T X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNeCcWttzRzieDiiYMXVdBZKr3iabfA61m)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (J2 X14 (T X15 (L X14 X15 (J2 X14 (T X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 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, (I1 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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, (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (J2 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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT9eb7o4umvAxuv3q6sNg1oTY2qJq2LoVT)
(∀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 (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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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, (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, (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, (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, (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, ∀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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRjZiuPwpypPLN2y7m8ztK3c4ppoH4jJCq)
(∀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 (T X17 X18)) = I2 X16 (T X17 (R 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, (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, (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, (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, (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 (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 (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, (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, (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, (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, (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 (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 (T X16 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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, (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 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTDYryo9iyCHf326hf17J4qdoTyuGucHz2)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (T X14 (R X15 X16 (L X14 X15 (I1 X16 (T X14 (R X15 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 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (R 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, (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, (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 (I2 X17 X18))) = I2 X16 (I2 X17 (J2 X14 (I2 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, (L X14 X15 (T X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀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, ∀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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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, (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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (T X16 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMacAQdPcsxfJxgYov6P5rqf4dVxP72MCpF)
(∀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, (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 (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (I2 X14 (I2 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 (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, (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, (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, ∀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 (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQMNLgwfLq66VbSgL7L5Ah4ZVtxhStnmVx)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀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 (T X17 X18)) = T X16 (T X17 (L X14 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, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T 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 (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 (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, ∀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 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFsXarPpmqZuUWWxTsKp9YVXWE511qZfUu)
(∀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 (R X14 X15 (T X16 (L X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀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 (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, (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 (T X16 (J2 X17 X18)) = T X16 (J2 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 (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 (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 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (J2 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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFxi4npm42zsMyNUtn7PXuRdjsNCa9fTWz)
(∀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 (R X14 X15 (I2 X16 (J2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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, (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 (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 (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, (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 (I1 X17 X18))) = J2 X16 (I1 X17 (I2 X14 (T 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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (T 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 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGUA8NNBv5DkPRNyiTBQxzEwaptsS6bcwk)
(∀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 (R X14 X15 (I2 X14 (I1 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, (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 (T X17 X18)) = I1 X16 (T X17 (R X14 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, (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, (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, (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, (J2 X14 (J2 X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (J2 X14 (J2 X15 X18))))) → (∀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, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 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 (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 (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, ∀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, (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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, (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbF5PnsUD1Jpwu6Li2fdcKMfH7W49bs978)
(∀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 (I2 X15 (I1 X16 X17)) = I2 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, (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, (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, (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 X14 (I1 X15 X18))))) → (∀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, (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 (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, (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, ∀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 (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)))))) → (∀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 (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 (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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVBfJZzr3evh63DtpiqzxAjGPKzdY2jqzq)
(∀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, (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 (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 (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 (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, (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 (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 (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 (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, (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, (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, ∀X21 ∈ X, (R X14 X15 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (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 (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 (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, (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, (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, (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbt9Q4SgadWHcQobcE4akPVDrvj2QMLxzx)
(∀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, (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T 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 (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 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (T X14 (T 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 (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, (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, ∀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 (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 (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 (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, (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 (T X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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 (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, (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 (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 (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 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKY5aqT1GBTxmEPR6GbKMKu6TmdTnL9gF7)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 X16)))))))) = X16)) → (∀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, (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, (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 (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 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 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 (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, (L X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L 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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFLq6G2dnQqtbQ6LxfJF2y1eEJ45jH83ug)
(∀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 (I1 X16 (R X14 X15 (I1 X16 (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, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 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, (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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (J2 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMchYmh1883VNFovbpZVREWnG5om9rPTUhz)
(∀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 (L X14 X15 (I2 X16 (R X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀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, (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, (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, (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, (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 (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 (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, ∀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 (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZMeSx9goa46B8CgR5KD4NtMuh9oWeurfX)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 X16))))))))))) = X16)) → (∀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, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 X16 (T 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, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (T 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, (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, (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 (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (I1 X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT8RXhPk92qNE6fTgvHKem1g6VGpF4sJWp)
(∀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, (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, (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 (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 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T 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, (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 (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 (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, (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 (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, (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 (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, (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 (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 (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 (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 (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, (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGCaXU3NfuqRJ7Q284a47N8wGLBLxvdLjK)
(∀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 (L X14 X15 (I2 X16 (R X14 X15 (I2 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, (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, (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 (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, (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, (I2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, ∀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, (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 (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 (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, ∀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, (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)))))) → (∀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 (J2 X20 X21)))) = L 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 (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 (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, (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLVLSBQ1a4Ui7BRyevd5gCYFV1vtuGNGtm)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T 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, (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (I2 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, (T X14 (J2 X15 (J2 X16 (I1 X17 X18))) = J2 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, ∀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, (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 (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, (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 (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 (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)))))) → (∀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 (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 (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 (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 (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 (I2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJVM9B3Q8qs77yvVajxmDztSfnt1kEwp1P)
(∀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 (R X14 X15 (T X16 (L X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀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 (L X14 X15 (T X16 (R X14 X15 (T X16 X17))))))))))))))) = X17)) → (∀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 (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 (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 (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 (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, (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, (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, ∀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 (I1 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQkDo4UiYNm6FsQB8SEfXDJ475o1QbkYxq)
(∀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, (I1 X14 (I1 X15 (I2 X16 X17)) = I1 X15 (I2 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 (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, (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 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (T 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, (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, ∀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 (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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (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 (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, (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXiFveASuh7k527w41hzbJMu62b3vvm57R)
(∀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, (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 (L X14 X15 (J2 X16 X17))))))))))))))) = X17)) → (∀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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 X14 (T 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, (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, (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, (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 (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 (I2 X16 (J2 X17 (J2 X18 X19))) = J2 X17 (J2 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 (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, (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 (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 (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 (T X20 X21)))) = L 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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T 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 (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 (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 (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 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHqQ5KxzifyCmwiaDUVuvcFJywFRmEqD7S)
(∀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 (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, (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, (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 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (R 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, (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 (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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, (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, (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, ∀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, (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 (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 (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 (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 (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 (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, (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 (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, (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 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYsvKjkCyUtvXq186ffbwGASnyfuPwmwkV)
(∀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, (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, (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 (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 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (T 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, (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 (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, (I1 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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 (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 (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, (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 (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, (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWh4hwThakVUHZ6dQx2WNLFyUXS2dunTJv)
(∀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, (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 (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 (T X17 X18)) = T X16 (T X17 (L X14 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, (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 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (I1 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (J2 X16 (T X17 (I1 X18 X19))) = T X17 (I1 X18 (R X14 X15 (J2 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, (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 (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 (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 (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 (T X20 X21)))) = L 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, (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMnbbvWBUCQkdec9HcDK7uYycA26gJvTKJ)
(∀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 (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 (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 (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, (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 (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, (J2 X14 (J2 X15 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (J2 X14 (J2 X15 X18))))) → (∀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, (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, ∀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 (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 (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, (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, (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKfwXoTD8TNxHMMYTeaXPcgErUdZNdNtdk)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 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 (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, (J2 X14 (I2 X15 (J2 X16 X17)) = I2 X15 (J2 X16 (J2 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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 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, (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, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (T X17 (I2 X18 X19))) = T 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWJye4cGrGT7fd6rUpie7Qn6eHQUkWPZPH)
(∀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, (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 X16 (L X14 X15 (I1 X16 (L X14 X15 (J2 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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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, (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, (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, (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, (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, (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, (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 (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 (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 (T X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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 (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMEu4bTGdtaw9HVHLxRsGZwCeivfbGoUroM)
(∀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 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 (R X14 X15 (T X14 (I1 X15 X16))))))))))) = X16)) → (∀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 (J2 X16 (T X17 X18)) = J2 X16 (T X17 (R X14 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 (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 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (I2 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, (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZMa7Xejt4eUgx1aapw2izBg1FoXAuVFrm)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 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, (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, (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 (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 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T 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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (I1 X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdtg9VdKmCELoGzwTBTaDDyTwG3d1U1ZRT)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 X16 (I1 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 (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 (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, (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, (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 (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, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMPeCmK7Bv3GxgLjRhJcFqYxiZvWEwu5Gf)
(∀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, (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, (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, (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, (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 (T X16 (I1 X17 X18))) = T 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 (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, (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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R 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 (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 (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, (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUriERbR3F9TreXxec8n2XxdWRFqCNMJFa)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 X17))))))) = X17)) → (∀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 (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 (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 (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 (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, (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 (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 (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, (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, ∀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 (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 (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 (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, (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, (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 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVwUXppRjQpVS36DM4xJW8ATinqKoHbMri)
(∀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, (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 X17))))))) = X17)) → (∀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, (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 (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, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I2 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, (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, (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 (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, (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, ∀X20 ∈ X, (R X14 X15 (I1 X16 (L X17 X18 (J2 X19 X20))) = L X17 X18 (J2 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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMX6kTUqqLPQRpcqvbw1QtJqiriJAHs7u1z)
(∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (J2 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, (J2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (T 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, (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, ∀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, (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, ∀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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcDCXmGD9fXYbknuS4mA4fCVqaYukFi9ND)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 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 (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 (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, (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 (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, (J2 X14 (J2 X15 (T X16 (T X17 X18))) = T X16 (T 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 (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 (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T 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 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ38q52DUGAdAPcYZx4dC1xVstrxbacGdc)
(∀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 (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, (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T 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 (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 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 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 (T X17 X18))) = I2 X16 (T X17 (J2 X14 (I1 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, (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, (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 (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, (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJVXKk1PP26qdLus83R78RkF2PdvmuwoXz)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (T X15 (R X14 X15 (I1 X14 (T X15 X16))))) = X16)) → (∀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, (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, (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 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (T 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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (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 (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 (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 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRhDjB5CSa1MQSbcUTg15w6mmdqqE22bjk)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀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 (L X14 X15 (T X16 (I1 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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, (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, (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, (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 (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 (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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXVeyAUUVP9zVPde9MyrMbe2PpvDJVa8WT)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 (R X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 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 (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 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 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, (T X14 (T X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I2 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, (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXAqpMUi9sL2qz6d6CbqvueEQ5Ca4cjxhK)
(∀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 (T X16 X17)) = I1 X15 (T X16 (I2 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, (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, (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, (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, (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 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I1 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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXtsGthEdfWDs8jk1TtYxzRQZmEQJczjnE)
(∀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, (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, (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 (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, (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 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 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, ∀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 (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, (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R 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 (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, (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVHsZVx6r8rw7abxNgvjBmnsH2rSKmCrGX)
(∀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 X16)))))))) = X16)) → (∀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 (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 (I2 X16 X17)) = I2 X15 (I2 X16 (T 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 (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, (T X14 (J2 X15 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (T 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, (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, (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, ∀X19 ∈ X, (R X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 X17 (I2 X18 (R 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, (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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdFm7f8VpsVjpGbvDHHCHFzaAuWRKw8Ug1)
(∀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, (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, (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 (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 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 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, (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 (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 (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXtwvqrXWRcxQJ4pQc7JZaDtdUG2X1xdzx)
(∀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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (J2 X14 (J2 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 (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, (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 (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I1 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMQe7ERMdyZUHfBpmasEMWMmoVLyrEaz1fr)
(∀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, (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 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, (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 (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 (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, (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 (I1 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (I1 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, ∀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, (L X14 X15 (I2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXr9nspLNc79i6Yf8L1FnLRMmUN8kY5DGq)
(∀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, (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 X16 (R X14 X15 (J2 X16 (L X14 X15 (I1 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, (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, (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 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (J2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 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, (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, (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, ∀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, (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 (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 (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 (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 (J2 X20 X21)))) = R 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 (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 (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, (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXWTKCJYuURHDtjTjq5S7hETE6Fz5PKRTL)
(∀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, (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 (I1 X17 X18)) = I1 X16 (I1 X17 (R X14 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, (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 (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (T 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 (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 (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 (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, (L X14 X15 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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, (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMM5pRyS2MZenKeUevxQW78poDhEFC9WXNe)
(∀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 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (I1 X17 X18)) = I2 X16 (I1 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, (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 (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 (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, (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, ∀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 (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, (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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L 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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (T X16 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMb13A84b3oeLuAJ1CR2dAh7DF9PaQA467N)
(∀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 X17))))))) = X17)) → (∀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, (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 (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 (J2 X16 (I2 X17 X18))) = J2 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 (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTuVsZbAAvuwSizqG5foShHLXfUZLscjbT)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 (R X14 X15 (I2 X14 (J2 X15 X16)))))))))))))) = X16)) → (∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T X16 (I2 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, (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, (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, (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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYqQ47TxcCqda3WyWAWbDWyqWaztkajUKQ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 (R X14 X15 (J2 X16 (R X14 X15 (I2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T 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 (I1 X16 (I2 X17 X18)) = I1 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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbWGMFajDRQPai4YejZJaJZnnFqiqjpaHk)
(∀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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 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, (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 (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, (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 (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, ∀X19 ∈ X, (R X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (R X14 X15 (I1 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 (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 (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (J2 X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (I2 X16 (I1 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWYrLBwaY3c8MZSBurqyTTmxTnskCzU7ZD)
(∀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 X17))))))) = X17)) → (∀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 (R X14 X15 (T X16 (I2 X14 (L X15 X16 (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, (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 (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 (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 (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, (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 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (T 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, (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, ∀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, (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, ∀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 (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, (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 (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 (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (I2 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUEkM1NMCji6JmaUU8SScLswo1cnwMMafR)
(∀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 (J2 X17 X18)) = T X16 (J2 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, (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, (T X14 (J2 X15 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (T 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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (I2 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 (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, (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, (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 (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, (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 (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 (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 (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, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMczFv156g4tbnW7riyymEVcT9vsonZFexe)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))) = X17)) → (∀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, ∀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 (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 (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 (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 (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 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (I1 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, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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 (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, (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, (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcHjqqcwNZ4TuWnuD5zwDVk3K3rwPocUUh)
(∀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, (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 (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 (T X17 X18))) = I1 X16 (T X17 (T 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, (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, (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, (L X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (I1 X18 X19))) = I2 X17 (I1 X18 (L 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 (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, ∀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 (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 (J2 X16 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T 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 (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 (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 (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 (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, (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 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMViyrLqKZozps4ebS2VBnJdNEJpsVUQD7b)
(∀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, (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 (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 (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 (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 (T X16 (I2 X17 X18))) = T X16 (I2 X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (J2 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 (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 (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 (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, (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 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVPRuBHd2Y6tNMsWxz7wpeZTd4XohCXgaf)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I2 X15 (L X14 X15 (T X14 (I2 X15 X16))))) = X16)) → (∀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 X17))))))))))) = X17)) → (∀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, (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, (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, (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 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I1 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, (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 (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 (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 (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 (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 (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 (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, (L X14 X15 (J2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R 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, (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 (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 (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 (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 (T X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbCffJY3MqtmzcbADDK4KwxeTfYniC5W9r)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))) = X17)) → (∀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 (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 (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 (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 (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, (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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 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 (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMM11qnAZK5XGa28esDUJsTE8JbmQeucg6r)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (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 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, (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 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (J2 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 (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 (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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMR7ox9BoWbhvZDJUcMfeGZCkVdZK5SaDAa)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 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, (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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 X17 (L X14 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, (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 (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, (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, (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, ∀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 (T X16 (I1 X17 (T X18 X19))) = I1 X17 (T 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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVBNzUAkkYhJQ1yTsyaimmmb2bAqRqZ4ey)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 (L X14 X15 (T X16 (I2 X14 (L X15 X16 X17))))))))))) = X17)) → (∀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 (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 (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 (J2 X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (J2 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 (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, (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, ∀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, (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 (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 (J2 X19 X20))) = L X17 X18 (J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKRVYVo15xD3MgnZcXQ2QmQGWXKbuVrFqC)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R X15 X16 (L X14 X15 (I2 X16 (I2 X14 (R 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, (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, (J2 X14 (I1 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (J2 X14 (I1 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, (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, (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 (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, ∀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, (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, ∀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 (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, ∀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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPHJxuKX9srk29dJUwEGm7feZayWH2NuTn)
(∀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 (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, (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, (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 (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 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I2 X14 (I2 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, (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 (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 (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, ∀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 (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 (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, (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 (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, (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 (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, (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPEpjsa7CBTXhLpTxCcp2cSFTVppge8aiz)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T X16 (R X14 X15 (T 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, (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 (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, (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, (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, (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, (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 (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, (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, (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 (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, ∀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 (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, (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 (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 (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 (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 (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 (T X16 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFx9NUrLnWtTEpVgmkwj5eMnh8vmHawFpb)
(∀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 (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, (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, (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, (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, (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, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 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 (T X18 X19))) = T 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMX2WX6atmh3QARbGccMViBSdhjNz2JYQqb)
(∀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 (J2 X16 (I1 X17 X18)) = J2 X16 (I1 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, (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 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, (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUopcBekmNJ94mTXA2NrxWh9cb3vDPjsSs)
(∀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, (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, (T X14 (J2 X15 (I1 X16 X17)) = J2 X15 (I1 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, (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 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 (T X16 (T X17 X18))) = T X16 (T X17 (T 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, (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, (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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L 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 (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, ∀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)))))) → (∀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 (J2 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (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 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdnEnkQdGcWG2sia9NXAkv1rGkCHN2LYj1)
(∀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, ∀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, (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 (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 (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 (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 (T X17 X18))) = I2 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, (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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMEsBcLx36oZREkGgvi236Ped5f5PWUDkEH)
(∀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, (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 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 (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, (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, (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZ2hsk9zW5fxYyDLXEyPLbxqT4tGT746KN)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 (L X14 X15 (I1 X16 (R X14 X15 (I1 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 (R X14 X15 (I1 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (T X16 X17)) = J2 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, (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 (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 (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, (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 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 X15 X18))))) → (∀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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X16 (J2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWCn2rK6WwRoK2ejA9VTxXXrKTnFge5t3U)
(∀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 (L X14 X15 (I2 X16 (L X14 X15 (I2 X16 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (L X14 X15 (I2 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (T X16 X17)) = J2 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, (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, (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, (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, (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 (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, (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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMPyRF7MwuT4NDEKyokauUVKxWWJAUTunwS)
(∀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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 (L X14 X15 (I2 X16 (R X14 X15 (J2 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I2 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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, (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, (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, (T X14 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (I1 X18 X19))) = I1 X17 (I1 X18 (L X14 X15 (J2 X16 X19))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (I1 X16 (T X17 (I1 X18 X19))) = T 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUzJbgH2FqzjkhWtGwK5BfDxeYBPHSEK8Z)
(∀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, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I2 X14 (L X15 X16 (R X14 X15 (J2 X16 (I2 X14 (L 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 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 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, (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, (I1 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 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 (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 (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, (R X14 X15 (J2 X16 (J2 X17 (T X18 X19))) = J2 X17 (T X18 (R X14 X15 (J2 X16 X19))))) → (∀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, (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 (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 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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, (L X14 X15 (I1 X16 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTiwKMvXD4fjYvchaWPVoWRbnfNthTrXnD)
(∀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 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 (I2 X16 (I1 X17 X18)) = I2 X16 (I1 X17 (R X14 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, (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, (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, (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (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 (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 (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdCsNGQEbQUQ2SXVN1qT2ggrqD5to46VSn)
(∀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 (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, (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, (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 (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, (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀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, ∀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, (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, ∀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 (T X16 (T X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (T X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHJ3LZnP9YueotzB2VcEyb2BCcb4t913GQ)
(∀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, (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, (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 (T X16 (I1 X17 X18)) = T X16 (I1 X17 (R X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (J2 X14 (I2 X15 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 X14 (I2 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 (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, (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, (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, (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 (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, (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 (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, ∀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 (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 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMRiW4LAMaMHYrJBvSY37xQcC2ASg3A1dzv)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 (R X14 X15 (I1 X16 (T X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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, (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 (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 (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 (T X16 (T X17 X18))) = T X16 (T X17 (I2 X14 (T 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 (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, (L X14 X15 (J2 X16 (T X17 (I2 X18 X19))) = T 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 (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, (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 (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, (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 (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, (L X14 X15 (I2 X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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, (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TML2TXTAspvRFRXqnsVFFLh4qpHU4MQ2eaM)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (R X14 X15 (T X16 (R X14 X15 (I2 X16 (R X14 X15 (T X16 X17))))))))))))))))))) = X17)) → (∀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, (T X14 (T X15 (I2 X16 X17)) = T X15 (I2 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, (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, (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, (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, (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, (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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJJBtZXmvHY3y2LG2wSkkph3kKG8KL7qCA)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (T X16 (I2 X14 (R X15 X16 (L X14 X15 (T X16 (I2 X14 (R X15 X16 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (J2 X14 (I1 X15 (R X14 X15 (J2 X14 (I1 X15 X16))))) = X16)) → (∀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, (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, (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, (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 (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 (I1 X16 (I1 X17 X18))) = I1 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 (I1 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (I1 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, (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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYUTuBgPJSQa1vrhUx2caPT5b1Gn25kbvr)
(∀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 X17))))))) = X17)) → (∀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, ∀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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (I2 X14 (I2 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 (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, (I1 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I1 X14 (J2 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 (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, (L X14 X15 (I2 X16 (J2 X17 (I1 X18 X19))) = J2 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 (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 (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 (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 (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 (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, (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, (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 (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, (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 (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 (T X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdrFQ4Sz2LG8kiB185ZZQVayygFq6UGi9M)
(∀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, (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 (J2 X16 X17)) = I1 X15 (J2 X16 (T X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (R X14 X15 (T X16 (J2 X17 X18)) = T X16 (J2 X17 (R 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, (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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (T X14 (I1 X15 X18))))) → (∀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, (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVGhqcNuNGWobteNDQjSK32QnaYpYshpfa)
(∀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 (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, (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, ∀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, (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, (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, (I2 X14 (J2 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 X14 (J2 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 (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 (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, ∀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, (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWjMF99gPJLEyJEirz3iipsMKAAQNyxi7r)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 (L X14 X15 (J2 X16 (I2 X14 (L X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (T X15 (L X14 X15 (T X14 (T 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 (I1 X16 (I2 X17 X18)) = I1 X16 (I2 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, (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, (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, (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 (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, ∀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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (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 (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 (J2 X16 (I1 X17 (L X18 X19 (T X20 X21)))) = L 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, (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMU2RCKttVQC1oMn69DtgekwTFbdeJSj3Gf)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L X15 X16 (R X14 X15 (I2 X16 (I1 X14 (L 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, (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 (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, (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, (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 (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (T X17 (J2 X18 X19))) = T 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 (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, (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, (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 (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 (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 (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 (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, (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, (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (T X16 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMNRN9esPTgksVEqQf4158DLtJxijYDadNn)
(∀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 X16)))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T 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, (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, (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, (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, ∀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, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T X18 (L X14 X15 (J2 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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMaGXbgcVgzUma4sdx5TVWT4wy77ougpa8w)
(∀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 (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, (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 (I1 X17 X18)) = I2 X16 (I1 X17 (L 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, (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 (T X16 (I1 X17 X18))) = T X16 (I1 X17 (T X14 (J2 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, (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, ∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMXZooFpFpQ1dzYq3KSqKhRLhjbirfUbt1A)
(∀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 X16))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T X14 (I1 X15 (L X14 X15 (T 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 (T X16 (I1 X17 X18)) = T X16 (I1 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, (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, (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, (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (I2 X14 (I2 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 (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, (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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUmsASg4ZLYfSNpFWrT482v2XSvQfnzv3b)
(∀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 (J2 X16 (I2 X17 X18)) = J2 X16 (I2 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, (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 (J2 X17 X18))) = I1 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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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, (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbBVm1B81StuCAdeGBhBfR7gLpjgfzP2Ue)
(∀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 (R X14 X15 (I1 X14 (T X15 X16)))))))))))))) = X16)) → (∀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, ∀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 (J2 X17 X18)) = I2 X16 (J2 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 (T X17 X18))) = I2 X16 (T X17 (J2 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, (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 (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, (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 (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, (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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMKPxqLZMy79spXZsTd6kGssK8WHRgm4HLL)
(∀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, (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 (I1 X15 (J2 X16 X17)) = I1 X15 (J2 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, (J2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (I2 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 (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 (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 (I2 X17 X18))) = T X16 (I2 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 (I2 X17 (T X18 X19))) = I2 X17 (T 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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUA8HPLNt3Y4KHBVVYWVzeZTtB6U52ruLh)
(∀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 (I1 X17 X18)) = T X16 (I1 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (T X15 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 X17 (I2 X14 (T 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, (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 (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 (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 (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 (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 (J2 X16 (R X17 X18 (I2 X19 X20))) = R X17 X18 (I2 X19 (L X14 X15 (J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMT3WwdmTaphrd2qBd45LLtAnTBu9CK5mZt)
(∀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, (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 (T X16 (T X17 X18))) = T X16 (T X17 (I1 X14 (T 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, (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, (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, ∀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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (J2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdVtb4rtvuFbR9rv2oTs8Z8dNf9vfmtvad)
(∀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 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, (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 (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 (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 (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 (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 (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 (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 (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 (J2 X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMdRqc3R8CK467qWAxytAfJe7vw7qKeivRD)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 X16 (R X14 X15 (T X16 (R X14 X15 (J2 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, (I2 X14 (I2 X15 (T X16 X17)) = I2 X15 (T X16 (I2 X14 X17)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (L X14 X15 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 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, (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 (I2 X16 (T X17 X18))) = I2 X16 (T X17 (T X14 (I1 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, (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, (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, (R X14 X15 (I2 X16 (J2 X17 (I2 X18 X19))) = J2 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 (I1 X16 (L X17 X18 (J2 X19 X20))) = L 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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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 (T X16 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF1HVbp1tsNkycLzDkxGU2Fw3cb7v1ZdGA)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T X16 (L X14 X15 (J2 X16 (R X14 X15 (T 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 (R X14 X15 (I2 X16 (I2 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀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 (I2 X17 X18)) = T X16 (I2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I1 X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I1 X14 (I1 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 (T X16 (I2 X17 X18))) = T 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, (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, (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 (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 (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 (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 (J2 X17 (L X18 X19 (I2 X20 X21)))) = L 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 (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 (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 (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 (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 (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 (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFoZd7GBpqB1HpHMzmxm7zeXkznxiDgk9c)
(∀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, (R X14 X15 (T X14 (I2 X15 (R X14 X15 (T 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 (I2 X17 X18)) = J2 X16 (I2 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, (J2 X14 (T X15 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (J2 X14 (T 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, (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, (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMajAqiLytx8iUosbTgeP94dPnjmoxmhVmK)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L X15 X16 (L X14 X15 (I2 X16 (I1 X14 (L 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 (L X14 X15 (J2 X16 (R X14 X15 (I2 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (J2 X15 (T X16 X17)) = J2 X15 (T 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, (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, (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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 X14 (I2 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, (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, ∀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 (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 (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, (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R 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 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 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 (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 (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, (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 (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 (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, (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 (I1 X16 (T X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMUypLEctZ2D2v4Muw7PAqnQHzwDDuG8NhY)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (J2 X16 X17)) = T X15 (J2 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, (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, (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 (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 (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 (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, (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 (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (T X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMchn1atbmoXFShN46a3rf9dfohZ48ZhBeo)
(∀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 X16))))))))))) = X16)) → (∀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 (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, ∀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 (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 (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, (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 (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, (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, (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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T X18 (L X14 X15 (J2 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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMbUUZMxmZdPTmRet4aZht3cqp5CD6u639B)
(∀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 X17))))))) = X17)) → (∀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, (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 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (R X14 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, (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 (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 (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, (J2 X14 (J2 X15 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 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 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 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 (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 (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, ∀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 (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 (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 (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, (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 (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 (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, (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSV816gUZWE77QszdJ4QQacBV3UF8XAEYF)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (L X14 X15 (I2 X14 (T X15 (L X14 X15 (I2 X14 (T X15 X16))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (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 (I2 X15 (I2 X16 X17)) = I2 X15 (I2 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 (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 (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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (T X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 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, ∀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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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, (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMae2p6ZdGYgETRnU7xrs776XzEa57Pstkw)
(∀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, (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, (T X14 (I1 X15 (J2 X16 X17)) = I1 X15 (J2 X16 (T 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, (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, (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, (T X14 (T X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T X14 (T 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 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (L X14 X15 (I1 X16 X19))))) → (∀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, ∀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, (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, (R X14 X15 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (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 (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 (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 (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, (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
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMa17gAeCqN9kwXNYz6YxLxX1QWrbfvQtQU)
(∀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 (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 (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 (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 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 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, (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, (R X14 X15 (I1 X16 (T X17 (J2 X18 X19))) = T X17 (J2 X18 (R X14 X15 (I1 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 (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, (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, (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (J2 X16 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMZJE4X4m42QmB5SrHVYEY6AJbKZoE2iDp5)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 (R X14 X15 (J2 X16 (I1 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (I1 X14 (T X15 (J2 X16 X17)) = T X15 (J2 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, (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, (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 (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, (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 (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, ∀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 (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, (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, (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 (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, (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 (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 (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 (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 (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, (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 (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 (I2 X16 (I2 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHgnuBvaQJYJn7hHRVyJaHybeWXDvAQRez)
(∀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, (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, (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, (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, (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, (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, (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, (L X14 X15 (T X16 (I1 X17 (T X18 X19))) = I1 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 (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 (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, (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, ∀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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (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 (J2 X16 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHGisMU1WQ8AzU1tadmezuuWtp94g2LTAz)
(∀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, (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 (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, (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, (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, (J2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (T 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, ∀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 (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 (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, (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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, (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWpudXmFd2C3LSybrr12QBB1AQ7XJKi95A)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 (L X14 X15 (I1 X16 (I1 X14 (R X15 X16 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (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 (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 X17))))))))))))))))))) = X17)) → (∀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 (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 (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, (T X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (T 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, (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, (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, ∀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 (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, (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, (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 (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 (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, (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 (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 (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 (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, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R 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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMWNm5W8GQVLYEtFv3ty6X59tmSreRH8MsS)
(∀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 X17))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (I1 X16 (J2 X14 (L X15 X16 (R X14 X15 (I1 X16 (J2 X14 (L X15 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 (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 (T X17 X18))) = I2 X16 (T X17 (I1 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 (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 (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 (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, ∀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, (L X14 X15 (I1 X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMF1doCmZnsRofQEtCGdFWkM9oVt4JxZQZu)
(∀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 (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 (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 (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, (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, (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, (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 (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 (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, (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMSHAgBW41CYTRKtc33RabXXXdwfChkHVY6)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (L X14 X15 (T X16 (L X14 X15 (I2 X16 (L X14 X15 (T 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, (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 (T X16 (I2 X17 X18)) = T X16 (I2 X17 (L X14 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 (T X17 X18))) = I2 X16 (T X17 (I1 X14 (J2 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 (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, (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, ∀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 (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 (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 (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 (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 (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 (J2 X16 (I2 X17 (L X18 X19 (T X20 X21)))) = L 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 (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 (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 (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 (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 (I2 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLtwr729Zrn3vkXnZ7iNftf4BgFCcXtFkd)
(∀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, (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 (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, (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 (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 (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, ∀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 (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, ∀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 (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, (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, (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 (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 (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 (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 (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 (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLyZD8YMyuTe4uxrybdB1e6XMAG5Q7jhfE)
(∀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 (R X14 X15 (T 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 (L X14 X15 (I2 X14 (I2 X15 (L X14 X15 (I2 X14 (I2 X15 X16)))))))))))))) = X16)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (I1 X15 (J2 X16 X17)) = I1 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, (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, (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, (I1 X14 (J2 X15 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I1 X14 (J2 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 (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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (I1 X16 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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, (R X14 X15 (T X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMEogE9Vdz7AVCM1NrVGs5cgtQANxyX1fP9)
(∀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 (J2 X17 X18)) = T X16 (J2 X17 (R X14 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, (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 (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 (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 (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, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (J2 X18 X19))) = I1 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀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, ∀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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcWdZJxkYqns2KM8eVsdAQSwhqAgpJf23F)
(∀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, (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, (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 (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 (J2 X17 X18))) = I2 X16 (J2 X17 (I1 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, ∀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, (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 (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, (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, (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 (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 (T X16 (J2 X17 (R X18 X19 (J2 X20 X21)))) = R 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, (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 (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 (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 (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 (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMTeHGPHRtzVkmiJ6reMwvtSVdDXk4tBedw)
(∀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, (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 (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 (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, (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, (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, (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, (J2 X14 (T X15 (T X16 (T X17 X18))) = T X16 (T X17 (J2 X14 (T X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (L X14 X15 (T X16 (I1 X17 (I2 X18 X19))) = I1 X17 (I2 X18 (L X14 X15 (T 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMS9FP5byn1e4T8DakZEiSPSidwJVoD1j8g)
(∀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 (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 (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, (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 (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, (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 (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, (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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, (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, (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)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMU1rbM19oT5tj6JJEeYB1bYgutMHx7SLcx)
(∀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 (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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (T X14 (I2 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, (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 (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, ∀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 (T X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 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 (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 (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 (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 (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 (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 (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 (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 (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 (T X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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 (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 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMVTiMrPnsdAdzqhwZkt3CyUVWtAs2Qs1o6)
(∀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, (L X14 X15 (I2 X14 (I1 X15 (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, ∀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 (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, (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, (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, (I2 X14 (I1 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (I1 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I2 X14 (J2 X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (I2 X14 (J2 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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHNSjfZKMj5D2AbwhFBrxfYUdu33m5JJTn)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (L X14 X15 (J2 X16 (R X14 X15 (J2 X16 (L X14 X15 (J2 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, (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 (T X15 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (J2 X14 (T 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 (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 (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 (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, ∀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 (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, (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, (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 (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 (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 (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, (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 (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 (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 (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, (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 (J2 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMJSYuQFGzTTPN3UvUX2HPQuwhVXYyUpXTW)
(∀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, (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 (L X14 X15 (T X14 (J2 X15 X16))))))))))) = X16)) → (∀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 (T X16 (J2 X17 X18)) = T 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, (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, (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, (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, (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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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, (L X14 X15 (J2 X16 (I2 X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMYepB7nwFKaQicpNqrd8J8zogGjYDFw9R8)
(∀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 (I2 X16 (J2 X17 X18)) = I2 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (I1 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (I2 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 (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 (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, (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, (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 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 X18 (L X14 X15 (T X16 X19))))) → (∀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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (I1 X16 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMGMc1LwvYTjZDx5wRav3ZtcGSbKBVxDo64)
(∀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, (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 (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 (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 (T X17 X18))) = I2 X16 (T X17 (I2 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, (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 (I2 X17 X18))) = T X16 (I2 X17 (I2 X14 (I1 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, ∀X19 ∈ X, (L X14 X15 (J2 X16 (I1 X17 (T X18 X19))) = I1 X17 (T 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, (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, (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 (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 (J2 X16 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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, (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 (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 (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 (T X17 (R X18 X19 (I1 X20 X21)))) = R 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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMLykoow54YfKursJiMm2MSA6iuFhgaY5mm)
(∀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 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 (R X14 X15 (I2 X16 (J2 X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀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, (I2 X14 (J2 X15 (I1 X16 (T X17 X18))) = I1 X16 (T X17 (I2 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 (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, (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, (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 (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 (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 (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 (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, ∀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 (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 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L 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, (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 (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 (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMa2kCmQsdQXfP4sD6uTrS6swyx6qpL7nwQ)
(∀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, (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 (R X14 X15 (T X14 (T X15 X16))))))))))) = X16)) → (∀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, (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, (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 (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 (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, (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, (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 (T X16 (I2 X17 (J2 X18 X19))) = I2 X17 (J2 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 (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 (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, (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFVodQzXiNJTMbJF8hVteLtrNMugzW2Y1x)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 X16 (L X14 X15 (I2 X16 (J2 X14 (L X15 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 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 (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 (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 (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, (I1 X14 (J2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (I1 X14 (J2 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, (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, ∀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, (L X14 X15 (J2 X16 (I2 X17 (T X18 X19))) = I2 X17 (T 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X16 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMHubS8cWtwAsCw4KuGKJY1jxxaKq6U8Q7E)
(∀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, (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 (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 (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 (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 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (I2 X15 X18))))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, ∀X19 ∈ X, (R X14 X15 (T X16 (J2 X17 (I1 X18 X19))) = J2 X17 (I1 X18 (R X14 X15 (T 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, (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, (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 (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, (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, (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 (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 (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 (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 (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 (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 (T X16 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMcshNBD1aAUgXZ4DAKCbqvPKRnxcAwYicp)
(∀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 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, (L X14 X15 (I1 X16 (J2 X17 X18)) = I1 X16 (J2 X17 (L X14 X15 X18)))) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, ∀X18 ∈ X, (T X14 (T X15 (J2 X16 (T X17 X18))) = J2 X16 (T X17 (T X14 (T 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 (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, (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, (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, ∀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 (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 (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, (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, (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 (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 (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 (I2 X17 (R X18 X19 (J2 X20 X21)))) = R 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 (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 (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 (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 (T X16 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMFDcvuLQpQpZiebbu1UE9uuBT5nVPVY8iH)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 (L X14 X15 (I2 X16 (T X14 (R X15 X16 X17))))))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (L X14 X15 (J2 X16 (I1 X14 (L X15 X16 (L X14 X15 (J2 X16 (I1 X14 (L 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, (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 (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 (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, (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, (J2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 X14 (I2 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, ∀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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
Theorem. (
conj_AIM2_TMMFHmVKvTcmZSJsAeY1isu6XVnE6GGsrfw)
(∀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 (T X15 (I2 X16 X17)) = T X15 (I2 X16 (T 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 (I2 X16 (I1 X17 X18))) = I2 X16 (I1 X17 (J2 X14 (T 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, (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, (J2 X14 (I2 X15 (I1 X16 (J2 X17 X18))) = I1 X16 (J2 X17 (J2 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, ∀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 (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, (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 (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 (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 (I2 X16 (T X17 (L X18 X19 (J2 X20 X21)))) = L 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, (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 (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 (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 (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, (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 (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 (I1 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof:The rest of this subproof is missing.
∎
End of Section AIM2