Beginning of Section AIM1_03
L6Variable m b s : set → set → set
L8Variable K : set → set → set
L9Variable a : set → set → set → set
L10Variable T : set → set → set
L11Variable L R : set → set → set → set
L12Variable I1 J1 I2 J2 : set → set → set
L16Theorem. (
conj_AIM1_TMYwUVRAuHYXewPaesp7TDyd1mWGFNKzQwx)
(∀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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L20Theorem. (
conj_AIM1_TMSLr3QoK5wjtkgVffDUx3F24V8KWmnEA2N)
(∀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 X16))))))))))) = X16)) → (∀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, (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 (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 (T X17 X18))) = J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L24Theorem. (
conj_AIM1_TMQjLtYsEiAHagfrpXGKsN9sSrk7ZctKFus)
(∀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 (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 (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 (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 (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 (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 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (I1 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L28Theorem. (
conj_AIM1_TMP8zeVxnvNGhfPwgpLRRVTYbdh4EtkR4vF)
(∀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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L32Theorem. (
conj_AIM1_TMTE39m8yEbEP3V9kW5nULTdr4bdx3rrEyF)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L36Theorem. (
conj_AIM1_TMY8q9kto417VibJTqWfSY3cwVeH1SnXfLr)
(∀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, (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, (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L40Theorem. (
conj_AIM1_TMJi1AGfWMyKCnZuJcc3T3bnnqM4ZfgdoYs)
(∀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, (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L44Theorem. (
conj_AIM1_TMHrs5NZib6maSaRyuHvcKSNJ3Y2GVsJtmo)
(∀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, ∀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 (T X17 X18)) = I1 X16 (T X17 (R X14 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 (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 (I1 X17 X18))) = I2 X16 (I1 X17 (I1 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L48Theorem. (
conj_AIM1_TMdCacard4Ax94PQyxLyGjj8X2pi8ZQCM4x)
(∀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 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 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 (J2 X16 (I1 X17 X18)) = J2 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 (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 (T X17 X18))) = I2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L52Theorem. (
conj_AIM1_TMaCp1wBALU4GCxKJid53jYUvMft1HTpDL3)
(∀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 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 (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 (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 (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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L56Theorem. (
conj_AIM1_TMWSAGToA4GPS5vMrvGFEDz24C2tXpmcXDX)
(∀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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L60Theorem. (
conj_AIM1_TMScTmJ9wnRCAgRrNxMSsyPzRBwXFoqeSwp)
(∀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, (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 (R X14 X15 (I1 X16 (R 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L64Theorem. (
conj_AIM1_TMaA1cAFw6JfngE1byrPVrwJkHEDfDUftSz)
(∀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 (L X14 X15 (I1 X16 (T 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 (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 (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 (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 (I2 X17 X18))) = T 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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L68Theorem. (
conj_AIM1_TMNYUuSQsAZPLUTYGY7c4ah5evx5s8CiNiA)
(∀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 X17))))))) = X17)) → (∀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 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 (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, (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, (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 (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 (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L72Theorem. (
conj_AIM1_TMHQQTRDudPFY1tqx3DRi44XbnMkFa94APz)
(∀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 (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 (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 (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 (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L76Theorem. (
conj_AIM1_TMMHCAkRCeU4BVv8ug2qW1CbWEkAfasQyay)
(∀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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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: Proof not loaded.
L80Theorem. (
conj_AIM1_TMJ2y3JDQA18oj1BHbjRqxm1qv4nFZ9M2ep)
(∀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 (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, (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 (J2 X16 (I2 X17 X18))) = J2 X16 (I2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L84Theorem. (
conj_AIM1_TMTFoSec6wGYiuBPzmDe9jZGmAiR2ZqJwp1)
(∀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 (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 (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 (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 (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 (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 (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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (J2 X20 X21)))) = R X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L88Theorem. (
conj_AIM1_TMdaShNh1QgwfMsUg8tSxpeSU9HCVTJ12Uo)
(∀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, (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, (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 (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 (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 (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 (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 (J2 X17 X18))) = I2 X16 (J2 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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L92Theorem. (
conj_AIM1_TMaaD8E58jpNYPEvqm5RtiABqhKLwFNXMUo)
(∀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 (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 (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 (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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L96Theorem. (
conj_AIM1_TMXdnayAAWmGzAFV38Qk79GCSk4HbQTt7Az)
(∀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 (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 (I1 X17 X18))) = I1 X16 (I1 X17 (T 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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L100Theorem. (
conj_AIM1_TMVAHhWif5bR8D1Hujg7iJqse6E73CRHmhy)
(∀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 (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 (L X14 X15 (T X16 (L X14 X15 (T 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, (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 (I1 X17 X18))) = T X16 (I1 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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L104Theorem. (
conj_AIM1_TMP6KDtxpCDL369Fmd2WotNLZjq356sJ5xy)
(∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L108Theorem. (
conj_AIM1_TMcGK7aNaxGsF6e9fugVsG1AXBAVzQ22mud)
(∀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, (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 (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, (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, (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, (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 (I1 X17 X18))) = I1 X16 (I1 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, ∀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, (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 (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 (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 (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 (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 (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, (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L112Theorem. (
conj_AIM1_TMLs6cCojN8BKyCDz9X7hk2Y59AZm8vo7E9)
(∀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, (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 (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, (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 (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 (T X17 X18))) = I1 X16 (T X17 (I1 X14 (I1 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L116Theorem. (
conj_AIM1_TMSgFGitmUthBvhcbxJquKnPBpcSywjukuM)
(∀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 (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 (I1 X17 X18)) = I2 X16 (I1 X17 (L 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, (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 (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 (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 (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (T X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L120Theorem. (
conj_AIM1_TMVd5dNmCxqkxdHpa6XBgtncD6XvkfsGBMc)
(∀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 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 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 (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 (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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 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, (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L124Theorem. (
conj_AIM1_TMJ6A5WFR38i8fvavFvZGPCehm7ufAp9hXS)
(∀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 (R X14 X15 (I1 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, (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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L128Theorem. (
conj_AIM1_TMcjjT6ZvdHUPvj1RyGhynD7n8TAqqq6Ckj)
(∀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 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, (J2 X14 (T X15 (I1 X16 X17)) = T 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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (J2 X16 (T X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L132Theorem. (
conj_AIM1_TMLPLaf89gvt1zFqBnC4kcX5z4exZiY5nzM)
(∀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 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, (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L136Theorem. (
conj_AIM1_TMEhXvAmfgfETyukzLafmppib7wQDrdhEw4)
(∀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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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, (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)))))) → False
Proof: Proof not loaded.
L140Theorem. (
conj_AIM1_TMcuUKx4SdMiKwVEy1WB9tCEQewC8FxRGAg)
(∀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, ∀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 (T X17 X18)) = I1 X16 (T X17 (L 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 (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 (I1 X16 (I2 X17 X18))) = I1 X16 (I2 X17 (J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L144Theorem. (
conj_AIM1_TMFUvHiJhvcbfQn8xDnZ7d5g9uNTmuryxsx)
(∀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, (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 (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 (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, (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, (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 (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L148Theorem. (
conj_AIM1_TMajQ1TD9nTcUNKAv9XDRVJgC6q4W9u3YEU)
(∀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, (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 (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 (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 (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 (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 (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, ∀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 (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 (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, (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 (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 (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, (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 (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 (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 (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: Proof not loaded.
L152Theorem. (
conj_AIM1_TMTQ15cVe5rBr8P6pShpbrdWEdNfb35dxXJ)
(∀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, (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 (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, (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 (I2 X16 (I2 X17 X18))) = I2 X16 (I2 X17 (T X14 (J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L156Theorem. (
conj_AIM1_TMZxfsDXE1sJiMaHo5RPTvuy3XYQZPGJB63)
(∀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 (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 (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 (I1 X17 X18))) = J2 X16 (I1 X17 (I1 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L160Theorem. (
conj_AIM1_TMKMWYk65PSrYDE6dYm5rgkMpE3Q8PtW4oj)
(∀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 (R 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, (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 (I2 X17 X18)) = I1 X16 (I2 X17 (R X14 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L164Theorem. (
conj_AIM1_TMULMa62cxv6vxY6r3nKLLB5kYAKqeq6VeH)
(∀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 (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 (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 (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 (J2 X17 X18))) = I2 X16 (J2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L168Theorem. (
conj_AIM1_TMPwfqNyFMzbtD8wuDThexz2wzxEb7BwMpP)
(∀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, (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 (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, (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 (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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L172Theorem. (
conj_AIM1_TMFfBQWYAPd4FJSgcenPsbDvbyft4YzpTuC)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (T X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L176Theorem. (
conj_AIM1_TMKCayKZxMfG1P3yrg1LrKUJVeaL6VmCoiy)
(∀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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L180Theorem. (
conj_AIM1_TMd9xTYoDGbykaSrs45ekM2MwG4QZzbtk5Q)
(∀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, (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, (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, (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 (T X16 (J2 X17 X18))) = T X16 (J2 X17 (I2 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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (I2 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L184Theorem. (
conj_AIM1_TMQRyrNzueRAFF6bUmLoA3fkSkHmjN5JdPG)
(∀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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L188Theorem. (
conj_AIM1_TMKDU4tcbdfVeTqtycJ9nZdg7p1GdfhkyD4)
(∀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, (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 (I1 X17 X18))) = I1 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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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)))))) → (∀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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L192Theorem. (
conj_AIM1_TMGdDYoDau7gRUk8vb2AtgPnvbWczrrUcyL)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L196Theorem. (
conj_AIM1_TMNvsxDbBxK9YxUuw3nwrBQpXVuH8azdPdc)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L200Theorem. (
conj_AIM1_TMdepJJdhyrBEVNjfaNXRZqSb7BwopEsySy)
(∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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)))))) → (∀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 (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 (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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L204Theorem. (
conj_AIM1_TMciJzuEAEPTQD7wEjyNWG3GKxcGjwn3wDm)
(∀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, (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, (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 (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 (J2 X17 X18))) = I2 X16 (J2 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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L208Theorem. (
conj_AIM1_TMSqn38a7wuGK7RbP7uZmg93BcqHDb7KD61)
(∀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, ∀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, (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, (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (J2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L212Theorem. (
conj_AIM1_TMHPTYJxkySQqujZfrtjgZurHCBQDMGAe6t)
(∀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 (I1 X17 X18)) = J2 X16 (I1 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 (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 (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 (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, (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 (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 (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, (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 (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, (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 (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 (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, (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 (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 (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)))))) → False
Proof: Proof not loaded.
L216Theorem. (
conj_AIM1_TMac1KCKDkBaTk6W8JiJQBhLVPxSmnhpgwg)
(∀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 X17))))))))))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (J2 X14 (T X15 (I1 X16 X17)) = T X15 (I1 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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L220Theorem. (
conj_AIM1_TMYyRAGVCCErgRKem635UkwjdmZXp824sWL)
(∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L224Theorem. (
conj_AIM1_TMZ7yMw5TVBvmfcr5i22HaT4sBxBPv4ubhc)
(∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L228Theorem. (
conj_AIM1_TMYrYV6dQQETe3M5wDEUfLHMjZd6uVvF5Fs)
(∀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 (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 (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 (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, (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 (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 (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 (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 (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 (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, (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 (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 (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)))))) → (∀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 (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 (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 (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 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L232Theorem. (
conj_AIM1_TMYSkjE7xiE3AXWxrWpEYmrP3NUchqcdiL4)
(∀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 (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 (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 (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 (I1 X17 X18))) = I1 X16 (I1 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, (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L236Theorem. (
conj_AIM1_TMFDMizDofH2QFHLDWgGdQqv6a5wt4Lcpzd)
(∀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 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 (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 (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L240Theorem. (
conj_AIM1_TMR8X2cvoUCKiMYpciv6vEBhUoS2ntwMfbi)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L244Theorem. (
conj_AIM1_TMTdJQWxcghBsiiPdQPa5Ytm3jdSCBqyHQJ)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L248Theorem. (
conj_AIM1_TMcPvDrAMxjJAN62eQ8y3uocGtPt2GXmcFn)
(∀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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L252Theorem. (
conj_AIM1_TMWyzfBCcBFdNw8aXz81kdcV8qZuEp1wSFQ)
(∀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, (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 (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 (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 (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 (T X17 X18))) = T X16 (T X17 (I2 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L256Theorem. (
conj_AIM1_TMdBfeyjKAwovTiub2uBhAyGJ2jjr65zix4)
(∀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, (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L260Theorem. (
conj_AIM1_TMPiP1Trt7QosgVkHULQje8fpLxZyNsRCC8)
(∀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, (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, ∀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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L264Theorem. (
conj_AIM1_TMdnpPjfKz7YaKK6TSGyWT2UbHZhwnoWc7o)
(∀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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L268Theorem. (
conj_AIM1_TMXUX2UKB1tfeowuBLvWJHXgZefjSqZGwpk)
(∀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, (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, (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 (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 (J2 X16 (J2 X17 X18))) = J2 X16 (J2 X17 (J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L272Theorem. (
conj_AIM1_TMTuLFpGHVYQL6e6x8qgvo1dK4kezXyUiSw)
(∀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 (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 (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → False
Proof: Proof not loaded.
L276Theorem. (
conj_AIM1_TMJhoFjDnowfd3GRPKNT3aHCWkstsZpt9XT)
(∀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 (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 (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, (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 (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, (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 (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, (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L280Theorem. (
conj_AIM1_TMTJSZeiyrhXfrAit6jWwxBpNDwddddA4Uh)
(∀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, (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, (T X14 (J2 X15 (J2 X16 X17)) = J2 X15 (J2 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, (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 (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 (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L284Theorem. (
conj_AIM1_TMQN11eT3o7gjRYwkx3oPUWLWDMiPkHCaQJ)
(∀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 (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 (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, (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 (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L288Theorem. (
conj_AIM1_TMaAmzmxLTh7PTxBWgsfXPuhhBnuGmrQrdF)
(∀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, (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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L292Theorem. (
conj_AIM1_TMPDKivQifrukf2r5xKqHysSfXsJ9S4PmGK)
(∀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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (J2 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L296Theorem. (
conj_AIM1_TMKT18X65k3Li9TGP5yrVKb8kWq5qdiYoNB)
(∀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 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 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 (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 (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 (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 (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, ∀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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X17 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L300Theorem. (
conj_AIM1_TMGfRDeUkWTFhBRmDCfNeizfks9aRhCvDhZ)
(∀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, (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 (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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (J2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L304Theorem. (
conj_AIM1_TMQzCjxjtUQckQjhgAr8y6Y5bTppqyez6ew)
(∀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 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 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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L308Theorem. (
conj_AIM1_TMLYPD945dW8Ddtt6MpyaEScJRGrKSSLswp)
(∀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 X17))))))))))) = X17)) → (∀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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L312Theorem. (
conj_AIM1_TMX2BdTZX38u4zfxmYoEqR7pYt9JcBijJKK)
(∀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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L316Theorem. (
conj_AIM1_TMW5FFdXhxYAoBTCNgrjjnC1XDziHZgRdNp)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → (∀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 (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 (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 (I1 X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L320Theorem. (
conj_AIM1_TMG88UPg27rdiafJRnSshiHdT1bkn37Q6KP)
(∀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 (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 (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 (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 (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L324Theorem. (
conj_AIM1_TMWWAVQMcvf4zA3mjLwbQU8VjmthkRmcVch)
(∀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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L328Theorem. (
conj_AIM1_TMYzrcB4g8sg2kVR5J5fQkWt5MLp6RWoT96)
(∀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, ∀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 (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 (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 (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, (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (R X14 X15 (I2 X16 (J2 X17 X21)))))) → False
Proof: Proof not loaded.
L332Theorem. (
conj_AIM1_TMVNLxKPxZF3eaVFzf5yrcdaTbskVJJc79W)
(∀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, (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T X14 (R 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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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: Proof not loaded.
L336Theorem. (
conj_AIM1_TMY2rHsrRtjdGSwDEA3CZM25PPM5deLX5S5)
(∀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, (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 (T X17 X18))) = I2 X16 (T 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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (L X18 X19 (J2 X20 X21)))) = L X18 X19 (J2 X20 (R X14 X15 (I2 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L340Theorem. (
conj_AIM1_TMbpZufNWnsJ6Vdgc8jwo5n9NBmf3WATx1s)
(∀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 (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 (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 (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, (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L344Theorem. (
conj_AIM1_TMbrB3Xgup6JLQzi9nyjB6TdN5KEq8MpvpE)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (T X20 X21)))) = L X18 X19 (T X20 (L X14 X15 (T X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L348Theorem. (
conj_AIM1_TMU5NE6XLRmmYxRdEZMdJVN4y7y1chGNixi)
(∀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, (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 (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 (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 (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 (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 (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 (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 (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, ∀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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I1 X20 X21)))) = R X18 X19 (I1 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L352Theorem. (
conj_AIM1_TMGu7azDaVvgn7wW72prcFBzrhLkEdfP7mw)
(∀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, (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 (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 (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 (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 (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 (I1 X16 (I1 X17 X18))) = I1 X16 (I1 X17 (I2 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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (I2 X17 (L X18 X19 (I1 X20 X21)))) = L X18 X19 (I1 X20 (R X14 X15 (I1 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L356Theorem. (
conj_AIM1_TMNsnbqoazfEz8nXdwQ2WaKXH4nhxHNcFpQ)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T X14 (R X15 X16 (R X14 X15 (J2 X16 (T 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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L360Theorem. (
conj_AIM1_TMYGGSLeFnDzGSQejzwXKXR3SUmkWFJ4PdS)
(∀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, (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, (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, (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, (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 (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 (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, (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I2 X16 (I2 X17 X21)))))) → False
Proof: Proof not loaded.
L364Theorem. (
conj_AIM1_TMdrL7vCPN9cUpYq1Mz69gSu2tq3eDYWnaF)
(∀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, (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 (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 (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 (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, (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (J2 X20 X21)))) = R X18 X19 (J2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L368Theorem. (
conj_AIM1_TMU2xy7L8hrVUdoYURXuYSw4UkusyYjw32q)
(∀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, (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 (L X14 X15 (I1 X16 (T 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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L372Theorem. (
conj_AIM1_TMVkz1YJCfU8h38KQQ4YDqMZ4v9J8mCpUSZ)
(∀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 (L X14 X15 (I1 X16 (J2 X14 (R X15 X16 (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, (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L376Theorem. (
conj_AIM1_TMJdWG7mYeVZfWXHT12UEPVccUcgi2ppKbb)
(∀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 (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 (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 (I1 X17 X18))) = T X16 (I1 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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (T X20 X21)))) = R X18 X19 (T X20 (R X14 X15 (T X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L380Theorem. (
conj_AIM1_TMY5J9nHeDhhvMvoYEyUP9KBULqAYag8ZEz)
(∀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 (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 (I2 X16 (J2 X17 X18))) = I2 X16 (J2 X17 (J2 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, (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L384Theorem. (
conj_AIM1_TMYU6sWHLMiLFLFnTDLDVSw5AvcyjtFq3Fh)
(∀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 (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, (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 (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 (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 (I1 X17 X18))) = J2 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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (I1 X17 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L388Theorem. (
conj_AIM1_TMXvpSAuszY7AYxoGYdttqonzeCY3smTvn8)
(∀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, (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 (I2 X16 X17)) = I1 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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 X17 (T 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 (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 (I2 X17 X18))) = I2 X16 (I2 X17 (I1 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, (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 (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, (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 (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)))))) → (∀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 (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 (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 (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 (T X17 (L X18 X19 (T X20 X21)))) = L X18 X19 (T X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L392Theorem. (
conj_AIM1_TMNf6SvhVb9zYDqZTdoHRpRbjr7zbqv6CHh)
(∀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 X17))))))) = X17)) → (∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, (R X14 X15 (I1 X14 (J2 X15 (R X14 X15 (I1 X14 (J2 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 (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 (I1 X17 X18))) = I2 X16 (I1 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, (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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: Proof not loaded.
L396Theorem. (
conj_AIM1_TMMVH7iVhjUHNf9pPh1jsBAF3WhKhuCxW5p)
(∀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, (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 (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 (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 (I1 X17 X18))) = T X16 (I1 X17 (T 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, (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 (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 (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, (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 (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, (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 (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, (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 (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, (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 (I1 X17 (L X18 X19 (I2 X20 X21)))) = L X18 X19 (I2 X20 (L X14 X15 (I1 X16 (I1 X17 X21)))))) → False
Proof: Proof not loaded.
L400Theorem. (
conj_AIM1_TMMNncgPQSzHVwaoRpBRmVV7rwqV2BVRpMM)
(∀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 (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, (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, (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 (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 (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 (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 (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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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: Proof not loaded.
L404Theorem. (
conj_AIM1_TMRLjsV7RCFGid17ZdHnpMiibDyU9xwNucV)
(∀X14 ∈ X, ∀X15 ∈ X, ∀X16 ∈ X, ∀X17 ∈ X, (R X14 X15 (J2 X16 (I1 X14 (L X15 X16 (R X14 X15 (J2 X16 (I1 X14 (L X15 X16 (R X14 X15 (J2 X16 (I1 X14 (L X15 X16 (R X14 X15 (J2 X16 (I1 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 X17))))))) = X17)) → (∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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, (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 (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 (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 (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 (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 (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 (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 (R X18 X19 (I2 X20 X21)))) = R X18 X19 (I2 X20 (R X14 X15 (I2 X16 (T X17 X21)))))) → False
Proof: Proof not loaded.
L408Theorem. (
conj_AIM1_TMZwxkn5SvkS7WFLoDkp1ejtyFRQEjiVbzy)
(∀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 (I2 X15 (L X14 X15 (I2 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, (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 (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 (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 (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 (J2 X16 (I1 X17 X18))) = J2 X16 (I1 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, ∀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 (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 (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 (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 (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 (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 (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 (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 (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)))))) → (∀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 (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)))))) → False
Proof: Proof not loaded.
L412Theorem. (
conj_AIM1_TMY5AmCx1Hj2K38pBGJKDgBV37AByQneMuk)
(∀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 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 (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, (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 (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 (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 (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 (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, ∀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, (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 (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 (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 (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 (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 (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 (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 (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 (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 (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, (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: Proof not loaded.
End of Section AIM1_03