Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Theorem 013a2.. : ∀ x0 x1 : ι → ο . ∀ x2 x3 x4 x5 x6 x7 . (∀ x8 : ι → ο . x8 x2 ⟶ x8 x3 ⟶ x8 x4 ⟶ x8 x5 ⟶ x8 x6 ⟶ x8 x7 ⟶ ∀ x9 . x0 x9 ⟶ x8 x9) ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x1 x2 ⟶ x1 x3 ⟶ x1 x4 ⟶ x1 x5 ⟶ ∀ x8 x9 x10 : ι → ι . x8 x2 = x3 ⟶ x8 x3 = x2 ⟶ x8 x4 = x5 ⟶ x8 x5 = x4 ⟶ x9 x2 = x4 ⟶ x9 x3 = x5 ⟶ x9 x4 = x2 ⟶ x9 x5 = x3 ⟶ x10 x2 = x5 ⟶ x10 x3 = x4 ⟶ x10 x4 = x3 ⟶ x10 x5 = x2 ⟶ ∀ x11 : ι → ι → ι → ι → ο . (∀ x12 x13 . x0 x12 ⟶ x0 x13 ⟶ not (x11 x12 x13 x12 x13)) ⟶ (∀ x12 x13 x14 x15 . x11 x12 x13 x14 x15 ⟶ x11 x14 x15 x12 x13) ⟶ (∀ x12 x13 . x0 x12 ⟶ x0 x13 ⟶ not (x11 x12 x13 x7 x7)) ⟶ (∀ x12 x13 x14 x15 . x0 x12 ⟶ x1 x13 ⟶ x0 x14 ⟶ x1 x15 ⟶ not (x11 x12 x13 x14 x15) ⟶ not (x11 x12 (x8 x13) x14 (x8 x15))) ⟶ (∀ x12 x13 x14 x15 . x0 x12 ⟶ x1 x13 ⟶ x0 x14 ⟶ x1 x15 ⟶ not (x11 x12 x13 x14 x15) ⟶ not (x11 x12 (x9 x13) x14 (x9 x15))) ⟶ (∀ x12 x13 x14 x15 . x0 x12 ⟶ x1 x13 ⟶ x0 x14 ⟶ x1 x15 ⟶ not (x11 x12 x13 x14 x15) ⟶ not (x11 x12 (x10 x13) x14 (x10 x15))) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x4 x6 x5 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x4 x6 x7 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x6 x6 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x7 x6 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x6 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x2 x2 x12 x7)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x2 x3 x12 x6)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x2 x12 x6)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x3 x12 x7)) ⟶ not (x11 x2 x2 x2 x3) ⟶ not (x11 x2 x2 x3 x4) ⟶ not (x11 x2 x2 x3 x5) ⟶ not (x11 x2 x2 x4 x2) ⟶ not (x11 x2 x2 x4 x3) ⟶ not (x11 x2 x2 x5 x2) ⟶ not (x11 x2 x2 x6 x2) ⟶ not (x11 x2 x2 x6 x3) ⟶ not (x11 x2 x3 x4 x2) ⟶ not (x11 x2 x3 x6 x2) ⟶ not (x11 x2 x6 x6 x5) ⟶ not (x11 x2 x7 x3 x3) ⟶ not (x11 x2 x7 x3 x4) ⟶ not (x11 x2 x7 x4 x2) ⟶ not (x11 x2 x7 x7 x4) ⟶ not (x11 x2 x7 x7 x5) ⟶ not (x11 x3 x2 x5 x2) ⟶ not (x11 x3 x2 x6 x2) ⟶ not (x11 x3 x2 x6 x5) ⟶ not (x11 x3 x2 x7 x4) ⟶ not (x11 x3 x2 x7 x5) ⟶ not (x11 x3 x3 x4 x6) ⟶ not (x11 x3 x4 x7 x2) ⟶ not (x11 x3 x5 x7 x2) ⟶ not (x11 x3 x6 x6 x5) ⟶ not (x11 x3 x7 x6 x5) ⟶ not (x11 x4 x2 x5 x2) ⟶ not (x11 x4 x2 x6 x2) ⟶ not (x11 x4 x3 x4 x6) ⟶ not (x11 x4 x3 x6 x2) ⟶ not (x11 x4 x7 x6 x5) ⟶ not (x11 x5 x2 x6 x2) ⟶ not (x11 x5 x2 x6 x5) ⟶ not (x11 x5 x2 x7 x4) ⟶ not (x11 x5 x2 x7 x5) ⟶ not (x11 x5 x3 x6 x2) ⟶ not (x11 x5 x4 x7 x2) ⟶ not (x11 x5 x5 x7 x2) ⟶ not (x11 x6 x2 x6 x3) ⟶ not (x11 x6 x2 x7 x4) ⟶ not (x11 x6 x5 x6 x7) ⟶ not (x11 x6 x5 x7 x2) ⟶ not (x11 x6 x5 x7 x6) ⟶ not (x11 x7 x2 x7 x3) ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ ∀ x16 . x0 x16 ⟶ x11 x6 x5 x2 x12 ⟶ x11 x6 x5 x13 x14 ⟶ x11 x6 x5 x15 x16 ⟶ x11 x2 x12 x13 x14 ⟶ x11 x2 x12 x15 x16 ⟶ x11 x13 x14 x15 x16 ⟶ False (proof)

Proofgold Address