Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Theorem 3f4ba.. : ∀ x0 x1 : ι → ι → ο . ∀ x2 . ∀ x3 : ι → ι . ∀ x4 x5 . ∀ x6 x7 : ι → ι → ι . ∀ x8 : ι → ι → ι → ι . ∀ x9 x10 : ι → ι → ι . ∀ x11 : ι → ι . ∀ x12 x13 . ∀ x14 : ι → ο . (∀ x15 x16 . x14 x16 ⟶ (x16 = x15 ⟶ False) ⟶ x14 x15 ⟶ False) ⟶ (∀ x15 x16 . x0 x15 x16 ⟶ x14 x16 ⟶ False) ⟶ (∀ x15 . x14 x15 ⟶ (x15 = x13 ⟶ False) ⟶ False) ⟶ (∀ x15 . (x1 x15 x15 ⟶ False) ⟶ False) ⟶ (x14 x12 ⟶ False) ⟶ ((x14 x2 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x0 x16 x15 ⟶ (x1 x16 (x11 x15) ⟶ False) ⟶ False) ⟶ (∀ x15 . x14 (x3 x15) ⟶ False) ⟶ ((x14 x13 ⟶ False) ⟶ False) ⟶ ((x14 x4 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . (x0 (x10 x16 x15) x15 ⟶ False) ⟶ (x0 (x9 x16 x15) x16 ⟶ False) ⟶ (x16 = x11 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . (x0 (x9 x16 x15) (x10 x16 x15) ⟶ False) ⟶ (x0 (x9 x16 x15) x16 ⟶ False) ⟶ (x16 = x11 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x0 (x9 x17 x16) x17 ⟶ x0 (x9 x17 x16) x15 ⟶ x0 x15 x16 ⟶ (x17 = x11 x16 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 x18 . x17 = x11 x18 ⟶ x0 x16 x15 ⟶ x0 x15 x18 ⟶ (x0 x16 x17 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x16 = x11 x17 ⟶ x0 x15 x16 ⟶ (x0 (x8 x15 x16 x17) x17 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x16 = x11 x17 ⟶ x0 x15 x16 ⟶ (x0 x15 (x8 x15 x16 x17) ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x0 (x7 x15 x16) x15 ⟶ (x1 x16 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . (x0 (x7 x15 x16) x16 ⟶ False) ⟶ (x1 x16 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x1 x16 x17 ⟶ x0 x15 x16 ⟶ (x0 x15 x17 ⟶ False) ⟶ False) ⟶ ((x13 = x4 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . (x6 x16 x15 = x15 ⟶ False) ⟶ (x0 (x6 x16 x15) x16 ⟶ False) ⟶ (x16 = x3 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x0 (x6 x16 x15) x16 ⟶ x6 x16 x15 = x15 ⟶ (x16 = x3 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x16 = x3 x17 ⟶ x15 = x17 ⟶ (x0 x15 x16 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 x17 . x16 = x3 x17 ⟶ x0 x15 x16 ⟶ (x15 = x17 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x1 x16 x15 ⟶ x1 x15 x16 ⟶ (x16 = x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x15 = x16 ⟶ (x1 x16 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x16 = x15 ⟶ (x1 x16 x15 ⟶ False) ⟶ False) ⟶ (∀ x15 x16 . x0 x15 x16 ⟶ x0 x16 x15 ⟶ False) ⟶ (x11 (x3 x5) = x5 ⟶ False) ⟶ False (proof)

Proofgold Address