Proofgold Asset

Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Known fc633.. : ∀ x0 : ι → ο . ∀ x1 x2 x3 x4 x5 x6 . (∀ x7 : ι → ο . x7 x1 ⟶ x7 x2 ⟶ x7 x3 ⟶ x7 x4 ⟶ x7 x5 ⟶ x7 x6 ⟶ ∀ x8 . x0 x8 ⟶ x7 x8) ⟶ x0 x1 ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ ∀ x7 : ι → ι → ι → ι → ο . (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x2 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x3 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x3 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x4)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x4)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x5)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x1 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x2 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x2 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x5 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x5 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x6 x8)) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x11 x12 x9 x10) ⟶ (∀ x9 x10 . x0 x9 ⟶ x0 x10 ⟶ x8 x9 x10 x6 x6) ⟶ (∀ x9 . x0 x9 ⟶ x8 x5 x5 x6 x9) ⟶ (∀ x9 . x0 x9 ⟶ x8 x5 x6 x6 x9) ⟶ x8 x1 x1 x1 x3 ⟶ x8 x1 x1 x1 x5 ⟶ x8 x1 x1 x2 x1 ⟶ x8 x1 x1 x2 x2 ⟶ x8 x1 x1 x2 x5 ⟶ x8 x1 x1 x3 x3 ⟶ x8 x1 x1 x3 x4 ⟶ x8 x1 x1 x3 x5 ⟶ x8 x1 x1 x4 x2 ⟶ x8 x1 x1 x4 x3 ⟶ x8 x1 x1 x4 x5 ⟶ x8 x1 x1 x5 x3 ⟶ x8 x1 x1 x5 x4 ⟶ x8 x1 x1 x6 x1 ⟶ x8 x1 x1 x6 x3 ⟶ x8 x1 x1 x6 x4 ⟶ x8 x1 x2 x1 x4 ⟶ x8 x1 x2 x1 x6 ⟶ x8 x1 x2 x2 x1 ⟶ x8 x1 x2 x2 x2 ⟶ x8 x1 x2 x2 x6 ⟶ x8 x1 x2 x3 x3 ⟶ x8 x1 x2 x3 x4 ⟶ x8 x1 x2 x3 x6 ⟶ x8 x1 x2 x4 x1 ⟶ x8 x1 x2 x4 x4 ⟶ x8 x1 x2 x4 x6 ⟶ x8 x1 x2 x5 x3 ⟶ x8 x1 x2 x5 x4 ⟶ x8 x1 x2 x6 x2 ⟶ x8 x1 x2 x6 x3 ⟶ x8 x1 x2 x6 x4 ⟶ x8 x1 x3 x1 x6 ⟶ x8 x1 x3 x2 x3 ⟶ x8 x1 x3 x2 x4 ⟶ x8 x1 x3 x2 x5 ⟶ x8 x1 x3 x3 x1 ⟶ x8 x1 x3 x3 x2 ⟶ x8 x1 x3 x3 x5 ⟶ x8 x1 x3 x4 x1 ⟶ x8 x1 x3 x4 x4 ⟶ x8 x1 x3 x4 x6 ⟶ x8 x1 x3 x5 x1 ⟶ x8 x1 x3 x5 x2 ⟶ x8 x1 x3 x6 x1 ⟶ x8 x1 x3 x6 x2 ⟶ x8 x1 x3 x6 x3 ⟶ x8 x1 x4 x1 x5 ⟶ x8 x1 x4 x2 x3 ⟶ x8 x1 x4 x2 x4 ⟶ x8 x1 x4 x2 x6 ⟶ x8 x1 x4 x3 x1 ⟶ x8 x1 x4 x3 x2 ⟶ x8 x1 x4 x3 x6 ⟶ x8 x1 x4 x4 x2 ⟶ x8 x1 x4 x4 x3 ⟶ x8 x1 x4 x4 x5 ⟶ x8 x1 x4 x5 x1 ⟶ x8 x1 x4 x5 x2 ⟶ x8 x1 x4 x6 x1 ⟶ x8 x1 x4 x6 x2 ⟶ x8 x1 x4 x6 x4 ⟶ x8 x1 x5 x2 x2 ⟶ x8 x1 x5 x2 x3 ⟶ x8 x1 x5 x3 x1 ⟶ x8 x1 x5 x3 x4 ⟶ x8 x1 x5 x3 x5 ⟶ x8 x1 x5 x3 x6 ⟶ x8 x1 x5 x4 x1 ⟶ x8 x1 x5 x4 x4 ⟶ x8 x1 x5 x4 x5 ⟶ x8 x1 x5 x4 x6 ⟶ x8 x1 x5 x5 x2 ⟶ x8 x1 x5 x5 x3 ⟶ x8 x1 x5 x6 x5 ⟶ x8 x1 x6 x2 x1 ⟶ x8 x1 x6 x2 x4 ⟶ x8 x1 x6 x3 x2 ⟶ x8 x1 x6 x3 x3 ⟶ x8 x1 x6 x3 x5 ⟶ x8 x1 x6 x3 x6 ⟶ x8 x1 x6 x4 x2 ⟶ x8 x1 x6 x4 x3 ⟶ x8 x1 x6 x4 x5 ⟶ x8 x1 x6 x4 x6 ⟶ x8 x1 x6 x5 x1 ⟶ x8 x1 x6 x5 x4 ⟶ x8 x1 x6 x6 x5 ⟶ x8 x2 x1 x2 x3 ⟶ x8 x2 x1 x2 x6 ⟶ x8 x2 x1 x3 x1 ⟶ x8 x2 x1 x3 x5 ⟶ x8 x2 x1 x4 x2 ⟶ x8 x2 x1 x4 x3 ⟶ x8 x2 x1 x4 x4 ⟶ x8 x2 x1 x4 x5 ⟶ x8 x2 x1 x5 x2 ⟶ x8 x2 x1 x5 x3 ⟶ x8 x2 x1 x5 x6 ⟶ x8 x2 x1 x6 x2 ⟶ x8 x2 x2 x2 x4 ⟶ x8 x2 x2 x2 x5 ⟶ x8 x2 x2 x3 x2 ⟶ x8 x2 x2 x3 x6 ⟶ x8 x2 x2 x4 x1 ⟶ x8 x2 x2 x4 x3 ⟶ x8 x2 x2 x4 x4 ⟶ x8 x2 x2 x4 x6 ⟶ x8 x2 x2 x5 x1 ⟶ x8 x2 x2 x5 x4 ⟶ x8 x2 x2 x5 x5 ⟶ x8 x2 x2 x6 x1 ⟶ x8 x2 x3 x2 x6 ⟶ x8 x2 x3 x3 x3 ⟶ x8 x2 x3 x3 x5 ⟶ x8 x2 x3 x4 x1 ⟶ x8 x2 x3 x4 x2 ⟶ x8 x2 x3 x4 x4 ⟶ x8 x2 x3 x4 x6 ⟶ x8 x2 x3 x5 x1 ⟶ x8 x2 x3 x5 x4 ⟶ x8 x2 x3 x5 x6 ⟶ x8 x2 x3 x6 x4 ⟶ x8 x2 x4 x2 x5 ⟶ x8 x2 x4 x3 x4 ⟶ x8 x2 x4 x3 x6 ⟶ x8 x2 x4 x4 x1 ⟶ x8 x2 x4 x4 x2 ⟶ x8 x2 x4 x4 x3 ⟶ x8 x2 x4 x4 x5 ⟶ x8 x2 x4 x5 x2 ⟶ x8 x2 x4 x5 x3 ⟶ x8 x2 x4 x5 x5 ⟶ x8 x2 x4 x6 x3 ⟶ x8 x2 x5 x2 x6 ⟶ x8 x2 x5 x3 x2 ⟶ x8 x2 x5 x3 x4 ⟶ x8 x2 x5 x4 x5 ⟶ x8 x2 x5 x4 x6 ⟶ x8 x2 x5 x5 x6 ⟶ x8 x2 x5 x6 x2 ⟶ x8 x2 x5 x6 x4 ⟶ x8 x2 x5 x6 x5 ⟶ x8 x2 x6 x3 x1 ⟶ x8 x2 x6 x3 x3 ⟶ x8 x2 x6 x4 x5 ⟶ x8 x2 x6 x4 x6 ⟶ x8 x2 x6 x5 x5 ⟶ x8 x2 x6 x6 x1 ⟶ x8 x2 x6 x6 x3 ⟶ x8 x2 x6 x6 x5 ⟶ x8 x3 x1 x3 x2 ⟶ x8 x3 x1 x3 x5 ⟶ x8 x3 x1 x4 x2 ⟶ x8 x3 x1 x4 x3 ⟶ x8 x3 x1 x4 x6 ⟶ x8 x3 x1 x5 x3 ⟶ x8 x3 x1 x5 x4 ⟶ x8 x3 x1 x6 x3 ⟶ x8 x3 x1 x6 x5 ⟶ x8 x3 x2 x3 x6 ⟶ x8 x3 x2 x4 x1 ⟶ x8 x3 x2 x4 x4 ⟶ x8 x3 x2 x4 x5 ⟶ x8 x3 x2 x5 x3 ⟶ x8 x3 x2 x5 x4 ⟶ x8 x3 x2 x6 x4 ⟶ x8 x3 x2 x6 x5 ⟶ x8 x3 x3 x3 x4 ⟶ x8 x3 x3 x3 x5 ⟶ x8 x3 x3 x4 x1 ⟶ x8 x3 x3 x4 x4 ⟶ x8 x3 x3 x4 x5 ⟶ x8 x3 x3 x5 x1 ⟶ x8 x3 x3 x5 x2 ⟶ x8 x3 x3 x6 x1 ⟶ x8 x3 x3 x6 x5 ⟶ x8 x3 x4 x3 x6 ⟶ x8 x3 x4 x4 x2 ⟶ x8 x3 x4 x4 x3 ⟶ x8 x3 x4 x4 x6 ⟶ x8 x3 x4 x5 x1 ⟶ x8 x3 x4 x5 x2 ⟶ x8 x3 x4 x6 x2 ⟶ x8 x3 x4 x6 x5 ⟶ x8 x3 x5 x1 x6 ⟶ x8 x3 x5 x3 x6 ⟶ x8 x3 x5 x5 x2 ⟶ x8 x3 x5 x5 x4 ⟶ x8 x3 x6 x5 x1 ⟶ x8 x3 x6 x5 x3 ⟶ x8 x4 x1 x4 x2 ⟶ x8 x4 x1 x4 x5 ⟶ x8 x4 x1 x5 x3 ⟶ x8 x4 x1 x5 x6 ⟶ x8 x4 x1 x6 x1 ⟶ x8 x4 x1 x6 x2 ⟶ x8 x4 x1 x6 x5 ⟶ x8 x4 x2 x4 x6 ⟶ x8 x4 x2 x5 x4 ⟶ x8 x4 x2 x5 x5 ⟶ x8 x4 x2 x6 x1 ⟶ x8 x4 x2 x6 x2 ⟶ x8 x4 x2 x6 x5 ⟶ x8 x4 x3 x4 x4 ⟶ x8 x4 x3 x4 x6 ⟶ x8 x4 x3 x5 x1 ⟶ x8 x4 x3 x5 x6 ⟶ x8 x4 x3 x6 x3 ⟶ x8 x4 x3 x6 x4 ⟶ x8 x4 x3 x6 x5 ⟶ x8 x4 x4 x4 x5 ⟶ x8 x4 x4 x5 x2 ⟶ x8 x4 x4 x5 x5 ⟶ x8 x4 x4 x6 x3 ⟶ x8 x4 x4 x6 x4 ⟶ x8 x4 x4 x6 x5 ⟶ x8 x4 x5 x1 x6 ⟶ x8 x4 x5 x2 x6 ⟶ x8 x4 x5 x6 x2 ⟶ x8 x4 x5 x6 x3 ⟶ x8 x4 x6 x6 x1 ⟶ x8 x4 x6 x6 x4 ⟶ x8 x5 x1 x5 x3 ⟶ x8 x5 x1 x5 x4 ⟶ x8 x5 x1 x5 x6 ⟶ x8 x5 x1 x6 x1 ⟶ x8 x5 x1 x6 x2 ⟶ x8 x5 x2 x5 x3 ⟶ x8 x5 x2 x5 x4 ⟶ x8 x5 x2 x5 x5 ⟶ x8 x5 x2 x6 x1 ⟶ x8 x5 x2 x6 x2 ⟶ x8 x5 x3 x5 x6 ⟶ x8 x5 x3 x6 x3 ⟶ x8 x5 x3 x6 x4 ⟶ x8 x5 x4 x5 x5 ⟶ x8 x5 x4 x6 x3 ⟶ x8 x5 x4 x6 x4 ⟶ x8 x5 x5 x2 x6 ⟶ x8 x6 x1 x6 x4 ⟶ x8 x6 x2 x6 x3 ⟶ x8 x6 x5 x1 x6 ⟶ x8 x6 x5 x2 x6 ⟶ x8 x6 x5 x5 x6 ⟶ ∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ x7 x1 x1 x9 x4 ⟶ x7 x9 x4 x10 x11 ⟶ not (x8 x1 x1 x9 x4) ⟶ not (x8 x1 x1 x10 x11) ⟶ not (x8 x9 x4 x10 x11) ⟶ ∀ x12 : ο . (x9 = x1 ⟶ x10 = x1 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x1 ⟶ x10 = x4 ⟶ x11 = x4 ⟶ x12) ⟶ (x9 = x1 ⟶ x10 = x4 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x1 ⟶ x10 = x5 ⟶ x11 = x5 ⟶ x12) ⟶ (x9 = x1 ⟶ x10 = x5 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x1 ⟶ x10 = x6 ⟶ x11 = x5 ⟶ x12) ⟶ (x9 = x2 ⟶ x10 = x2 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x2 ⟶ x10 = x4 ⟶ x11 = x4 ⟶ x12) ⟶ (x9 = x2 ⟶ x10 = x4 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x2 ⟶ x10 = x5 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x2 ⟶ x10 = x6 ⟶ x11 = x5 ⟶ x12) ⟶ (x9 = x4 ⟶ x10 = x1 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x4 ⟶ x10 = x2 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x4 ⟶ x10 = x3 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x4 ⟶ x10 = x4 ⟶ x11 = x6 ⟶ x12) ⟶ (x9 = x4 ⟶ x10 = x5 ⟶ x11 = x6 ⟶ x12) ⟶ x12
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Theorem 27d9b.. : ∀ x0 : ι → ο . ∀ x1 x2 x3 x4 x5 x6 . (∀ x7 : ι → ο . x7 x1 ⟶ x7 x2 ⟶ x7 x3 ⟶ x7 x4 ⟶ x7 x5 ⟶ x7 x6 ⟶ ∀ x8 . x0 x8 ⟶ x7 x8) ⟶ x0 x1 ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ ∀ x7 : ι → ι → ι → ι → ο . (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x2 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x3 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x1)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x3 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x2)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x4 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x3)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x5 x9 x4)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x4)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ not (x7 x8 x6 x9 x5)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x1 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x2 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x1 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x2 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x2 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x3 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x3 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x4 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x4 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x5 x8 x5 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x5 x8)) ⟶ (∀ x8 . x0 x8 ⟶ not (x7 x6 x8 x6 x8)) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x11 x12 x9 x10) ⟶ (∀ x9 x10 . x0 x9 ⟶ x0 x10 ⟶ x8 x9 x10 x6 x6) ⟶ (∀ x9 . x0 x9 ⟶ x8 x5 x5 x6 x9) ⟶ (∀ x9 . x0 x9 ⟶ x8 x5 x6 x6 x9) ⟶ x8 x1 x1 x1 x3 ⟶ x8 x1 x1 x1 x5 ⟶ x8 x1 x1 x2 x1 ⟶ x8 x1 x1 x2 x2 ⟶ x8 x1 x1 x2 x5 ⟶ x8 x1 x1 x3 x3 ⟶ x8 x1 x1 x3 x4 ⟶ x8 x1 x1 x3 x5 ⟶ x8 x1 x1 x4 x2 ⟶ x8 x1 x1 x4 x3 ⟶ x8 x1 x1 x4 x5 ⟶ x8 x1 x1 x5 x3 ⟶ x8 x1 x1 x5 x4 ⟶ x8 x1 x1 x6 x1 ⟶ x8 x1 x1 x6 x3 ⟶ x8 x1 x1 x6 x4 ⟶ x8 x1 x2 x1 x4 ⟶ x8 x1 x2 x1 x6 ⟶ x8 x1 x2 x2 x1 ⟶ x8 x1 x2 x2 x2 ⟶ x8 x1 x2 x2 x6 ⟶ x8 x1 x2 x3 x3 ⟶ x8 x1 x2 x3 x4 ⟶ x8 x1 x2 x3 x6 ⟶ x8 x1 x2 x4 x1 ⟶ x8 x1 x2 x4 x4 ⟶ x8 x1 x2 x4 x6 ⟶ x8 x1 x2 x5 x3 ⟶ x8 x1 x2 x5 x4 ⟶ x8 x1 x2 x6 x2 ⟶ x8 x1 x2 x6 x3 ⟶ x8 x1 x2 x6 x4 ⟶ x8 x1 x3 x1 x6 ⟶ x8 x1 x3 x2 x3 ⟶ x8 x1 x3 x2 x4 ⟶ x8 x1 x3 x2 x5 ⟶ x8 x1 x3 x3 x1 ⟶ x8 x1 x3 x3 x2 ⟶ x8 x1 x3 x3 x5 ⟶ x8 x1 x3 x4 x1 ⟶ x8 x1 x3 x4 x4 ⟶ x8 x1 x3 x4 x6 ⟶ x8 x1 x3 x5 x1 ⟶ x8 x1 x3 x5 x2 ⟶ x8 x1 x3 x6 x1 ⟶ x8 x1 x3 x6 x2 ⟶ x8 x1 x3 x6 x3 ⟶ x8 x1 x4 x1 x5 ⟶ x8 x1 x4 x2 x3 ⟶ x8 x1 x4 x2 x4 ⟶ x8 x1 x4 x2 x6 ⟶ x8 x1 x4 x3 x1 ⟶ x8 x1 x4 x3 x2 ⟶ x8 x1 x4 x3 x6 ⟶ x8 x1 x4 x4 x2 ⟶ x8 x1 x4 x4 x3 ⟶ x8 x1 x4 x4 x5 ⟶ x8 x1 x4 x5 x1 ⟶ x8 x1 x4 x5 x2 ⟶ x8 x1 x4 x6 x1 ⟶ x8 x1 x4 x6 x2 ⟶ x8 x1 x4 x6 x4 ⟶ x8 x1 x5 x2 x2 ⟶ x8 x1 x5 x2 x3 ⟶ x8 x1 x5 x3 x1 ⟶ x8 x1 x5 x3 x4 ⟶ x8 x1 x5 x3 x5 ⟶ x8 x1 x5 x3 x6 ⟶ x8 x1 x5 x4 x1 ⟶ x8 x1 x5 x4 x4 ⟶ x8 x1 x5 x4 x5 ⟶ x8 x1 x5 x4 x6 ⟶ x8 x1 x5 x5 x2 ⟶ x8 x1 x5 x5 x3 ⟶ x8 x1 x5 x6 x5 ⟶ x8 x1 x6 x2 x1 ⟶ x8 x1 x6 x2 x4 ⟶ x8 x1 x6 x3 x2 ⟶ x8 x1 x6 x3 x3 ⟶ x8 x1 x6 x3 x5 ⟶ x8 x1 x6 x3 x6 ⟶ x8 x1 x6 x4 x2 ⟶ x8 x1 x6 x4 x3 ⟶ x8 x1 x6 x4 x5 ⟶ x8 x1 x6 x4 x6 ⟶ x8 x1 x6 x5 x1 ⟶ x8 x1 x6 x5 x4 ⟶ x8 x1 x6 x6 x5 ⟶ x8 x2 x1 x2 x3 ⟶ x8 x2 x1 x2 x6 ⟶ x8 x2 x1 x3 x1 ⟶ x8 x2 x1 x3 x5 ⟶ x8 x2 x1 x4 x2 ⟶ x8 x2 x1 x4 x3 ⟶ x8 x2 x1 x4 x4 ⟶ x8 x2 x1 x4 x5 ⟶ x8 x2 x1 x5 x2 ⟶ x8 x2 x1 x5 x3 ⟶ x8 x2 x1 x5 x6 ⟶ x8 x2 x1 x6 x2 ⟶ x8 x2 x2 x2 x4 ⟶ x8 x2 x2 x2 x5 ⟶ x8 x2 x2 x3 x2 ⟶ x8 x2 x2 x3 x6 ⟶ x8 x2 x2 x4 x1 ⟶ x8 x2 x2 x4 x3 ⟶ x8 x2 x2 x4 x4 ⟶ x8 x2 x2 x4 x6 ⟶ x8 x2 x2 x5 x1 ⟶ x8 x2 x2 x5 x4 ⟶ x8 x2 x2 x5 x5 ⟶ x8 x2 x2 x6 x1 ⟶ x8 x2 x3 x2 x6 ⟶ x8 x2 x3 x3 x3 ⟶ x8 x2 x3 x3 x5 ⟶ x8 x2 x3 x4 x1 ⟶ x8 x2 x3 x4 x2 ⟶ x8 x2 x3 x4 x4 ⟶ x8 x2 x3 x4 x6 ⟶ x8 x2 x3 x5 x1 ⟶ x8 x2 x3 x5 x4 ⟶ x8 x2 x3 x5 x6 ⟶ x8 x2 x3 x6 x4 ⟶ x8 x2 x4 x2 x5 ⟶ x8 x2 x4 x3 x4 ⟶ x8 x2 x4 x3 x6 ⟶ x8 x2 x4 x4 x1 ⟶ x8 x2 x4 x4 x2 ⟶ x8 x2 x4 x4 x3 ⟶ x8 x2 x4 x4 x5 ⟶ x8 x2 x4 x5 x2 ⟶ x8 x2 x4 x5 x3 ⟶ x8 x2 x4 x5 x5 ⟶ x8 x2 x4 x6 x3 ⟶ x8 x2 x5 x2 x6 ⟶ x8 x2 x5 x3 x2 ⟶ x8 x2 x5 x3 x4 ⟶ x8 x2 x5 x4 x5 ⟶ x8 x2 x5 x4 x6 ⟶ x8 x2 x5 x5 x6 ⟶ x8 x2 x5 x6 x2 ⟶ x8 x2 x5 x6 x4 ⟶ x8 x2 x5 x6 x5 ⟶ x8 x2 x6 x3 x1 ⟶ x8 x2 x6 x3 x3 ⟶ x8 x2 x6 x4 x5 ⟶ x8 x2 x6 x4 x6 ⟶ x8 x2 x6 x5 x5 ⟶ x8 x2 x6 x6 x1 ⟶ x8 x2 x6 x6 x3 ⟶ x8 x2 x6 x6 x5 ⟶ x8 x3 x1 x3 x2 ⟶ x8 x3 x1 x3 x5 ⟶ x8 x3 x1 x4 x2 ⟶ x8 x3 x1 x4 x3 ⟶ x8 x3 x1 x4 x6 ⟶ x8 x3 x1 x5 x3 ⟶ x8 x3 x1 x5 x4 ⟶ x8 x3 x1 x6 x3 ⟶ x8 x3 x1 x6 x5 ⟶ x8 x3 x2 x3 x6 ⟶ x8 x3 x2 x4 x1 ⟶ x8 x3 x2 x4 x4 ⟶ x8 x3 x2 x4 x5 ⟶ x8 x3 x2 x5 x3 ⟶ x8 x3 x2 x5 x4 ⟶ x8 x3 x2 x6 x4 ⟶ x8 x3 x2 x6 x5 ⟶ x8 x3 x3 x3 x4 ⟶ x8 x3 x3 x3 x5 ⟶ x8 x3 x3 x4 x1 ⟶ x8 x3 x3 x4 x4 ⟶ x8 x3 x3 x4 x5 ⟶ x8 x3 x3 x5 x1 ⟶ x8 x3 x3 x5 x2 ⟶ x8 x3 x3 x6 x1 ⟶ x8 x3 x3 x6 x5 ⟶ x8 x3 x4 x3 x6 ⟶ x8 x3 x4 x4 x2 ⟶ x8 x3 x4 x4 x3 ⟶ x8 x3 x4 x4 x6 ⟶ x8 x3 x4 x5 x1 ⟶ x8 x3 x4 x5 x2 ⟶ x8 x3 x4 x6 x2 ⟶ x8 x3 x4 x6 x5 ⟶ x8 x3 x5 x1 x6 ⟶ x8 x3 x5 x3 x6 ⟶ x8 x3 x5 x5 x2 ⟶ x8 x3 x5 x5 x4 ⟶ x8 x3 x6 x5 x1 ⟶ x8 x3 x6 x5 x3 ⟶ x8 x4 x1 x4 x2 ⟶ x8 x4 x1 x4 x5 ⟶ x8 x4 x1 x5 x3 ⟶ x8 x4 x1 x5 x6 ⟶ x8 x4 x1 x6 x1 ⟶ x8 x4 x1 x6 x2 ⟶ x8 x4 x1 x6 x5 ⟶ x8 x4 x2 x4 x6 ⟶ x8 x4 x2 x5 x4 ⟶ x8 x4 x2 x5 x5 ⟶ x8 x4 x2 x6 x1 ⟶ x8 x4 x2 x6 x2 ⟶ x8 x4 x2 x6 x5 ⟶ x8 x4 x3 x4 x4 ⟶ x8 x4 x3 x4 x6 ⟶ x8 x4 x3 x5 x1 ⟶ x8 x4 x3 x5 x6 ⟶ x8 x4 x3 x6 x3 ⟶ x8 x4 x3 x6 x4 ⟶ x8 x4 x3 x6 x5 ⟶ x8 x4 x4 x4 x5 ⟶ x8 x4 x4 x5 x2 ⟶ x8 x4 x4 x5 x5 ⟶ x8 x4 x4 x6 x3 ⟶ x8 x4 x4 x6 x4 ⟶ x8 x4 x4 x6 x5 ⟶ x8 x4 x5 x1 x6 ⟶ x8 x4 x5 x2 x6 ⟶ x8 x4 x5 x6 x2 ⟶ x8 x4 x5 x6 x3 ⟶ x8 x4 x6 x6 x1 ⟶ x8 x4 x6 x6 x4 ⟶ x8 x5 x1 x5 x3 ⟶ x8 x5 x1 x5 x4 ⟶ x8 x5 x1 x5 x6 ⟶ x8 x5 x1 x6 x1 ⟶ x8 x5 x1 x6 x2 ⟶ x8 x5 x2 x5 x3 ⟶ x8 x5 x2 x5 x4 ⟶ x8 x5 x2 x5 x5 ⟶ x8 x5 x2 x6 x1 ⟶ x8 x5 x2 x6 x2 ⟶ x8 x5 x3 x5 x6 ⟶ x8 x5 x3 x6 x3 ⟶ x8 x5 x3 x6 x4 ⟶ x8 x5 x4 x5 x5 ⟶ x8 x5 x4 x6 x3 ⟶ x8 x5 x4 x6 x4 ⟶ x8 x5 x5 x2 x6 ⟶ x8 x6 x1 x6 x4 ⟶ x8 x6 x2 x6 x3 ⟶ x8 x6 x5 x1 x6 ⟶ x8 x6 x5 x2 x6 ⟶ x8 x6 x5 x5 x6 ⟶ (x1 = x2 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x3 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x3 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x6 ⟶ ∀ x9 : ο . x9) ⟶ ∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ x7 x1 x1 x1 x4 ⟶ x7 x1 x4 x9 x10 ⟶ not (x8 x1 x1 x1 x4) ⟶ not (x8 x1 x1 x9 x10) ⟶ not (x8 x1 x4 x9 x10) ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x7 x9 x10 x11 x12 ⟶ not (x8 x1 x1 x11 x12) ⟶ not (x8 x1 x4 x11 x12) ⟶ not (x8 x9 x10 x11 x12) ⟶ ∀ x13 : ο . (x9 = x1 ⟶ x10 = x6 ⟶ x11 = x5 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x4 ⟶ x10 = x4 ⟶ x11 = x1 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x4 ⟶ x10 = x4 ⟶ x11 = x4 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x4 ⟶ x10 = x4 ⟶ x11 = x5 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x4 ⟶ x10 = x6 ⟶ x11 = x5 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x5 ⟶ x10 = x5 ⟶ x11 = x1 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x5 ⟶ x10 = x5 ⟶ x11 = x4 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x5 ⟶ x10 = x5 ⟶ x11 = x5 ⟶ x12 = x6 ⟶ x13) ⟶ (x9 = x6 ⟶ x10 = x5 ⟶ x11 = x4 ⟶ x12 = x6 ⟶ x13) ⟶ x13 (proof)