Proofgold Address

Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Known 26c4d.. : ∀ 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) ⟶ (∀ x8 . x0 x8 ⟶ not (x1 x8) ⟶ ∀ x9 : ι → ο . x9 x6 ⟶ x9 x7 ⟶ x9 x8) ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x6)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x2 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x7 x9)) ⟶ ∀ x9 : ι → ι → ι → ι → ο . (∀ x10 x11 . x0 x10 ⟶ x0 x11 ⟶ x9 x10 x11 x7 x7) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x6 x7 x10) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x7 x7 x10) ⟶ x9 x2 x6 x4 x6 ⟶ x9 x2 x6 x4 x7 ⟶ x9 x2 x6 x5 x6 ⟶ x9 x2 x6 x5 x7 ⟶ x9 x2 x6 x7 x6 ⟶ x9 x2 x7 x4 x7 ⟶ x9 x2 x7 x5 x7 ⟶ x9 x3 x6 x3 x7 ⟶ x9 x3 x6 x5 x6 ⟶ x9 x3 x6 x5 x7 ⟶ x9 x3 x6 x6 x7 ⟶ x9 x3 x6 x7 x6 ⟶ x9 x3 x7 x5 x7 ⟶ x9 x4 x6 x2 x7 ⟶ x9 x4 x6 x4 x7 ⟶ x9 x5 x6 x2 x7 ⟶ x9 x5 x6 x3 x7 ⟶ x9 x6 x6 x3 x7 ⟶ x9 x7 x6 x2 x7 ⟶ x9 x7 x6 x3 x7 ⟶ x9 x7 x6 x6 x7 ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x1 x10) ⟶ not (x1 x11) ⟶ not (x1 x12) ⟶ not (x1 x13) ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ ∀ x16 . x0 x16 ⟶ ∀ x17 . x0 x17 ⟶ x8 x14 x10 x15 x11 ⟶ x8 x15 x11 x16 x12 ⟶ x8 x16 x12 x17 x13 ⟶ not (x9 x14 x10 x15 x11) ⟶ not (x9 x14 x10 x16 x12) ⟶ not (x9 x14 x10 x17 x13) ⟶ not (x9 x15 x11 x16 x12) ⟶ not (x9 x15 x11 x17 x13) ⟶ not (x9 x16 x12 x17 x13) ⟶ ∀ x18 : ο . (x14 = x2 ⟶ x10 = x6 ⟶ x15 = x3 ⟶ x11 = x6 ⟶ x16 = x6 ⟶ x12 = x6 ⟶ x17 = x2 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x4 ⟶ x10 = x6 ⟶ x15 = x5 ⟶ x11 = x6 ⟶ x16 = x6 ⟶ x12 = x6 ⟶ x17 = x5 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x4 ⟶ x10 = x6 ⟶ x15 = x5 ⟶ x11 = x6 ⟶ x16 = x6 ⟶ x12 = x6 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x4 ⟶ x10 = x6 ⟶ x15 = x5 ⟶ x11 = x6 ⟶ x16 = x7 ⟶ x12 = x6 ⟶ x17 = x5 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x2 ⟶ x10 = x6 ⟶ x15 = x6 ⟶ x11 = x6 ⟶ x16 = x2 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x4 ⟶ x10 = x6 ⟶ x15 = x5 ⟶ x11 = x6 ⟶ x16 = x5 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x4 ⟶ x10 = x6 ⟶ x15 = x6 ⟶ x11 = x6 ⟶ x16 = x5 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x5 ⟶ x10 = x6 ⟶ x15 = x6 ⟶ x11 = x6 ⟶ x16 = x4 ⟶ x12 = x7 ⟶ x17 = x5 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x5 ⟶ x10 = x6 ⟶ x15 = x6 ⟶ x11 = x6 ⟶ x16 = x4 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x5 ⟶ x10 = x6 ⟶ x15 = x6 ⟶ x11 = x6 ⟶ x16 = x5 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x5 ⟶ x10 = x6 ⟶ x15 = x7 ⟶ x11 = x6 ⟶ x16 = x4 ⟶ x12 = x7 ⟶ x17 = x5 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x2 ⟶ x10 = x6 ⟶ x15 = x2 ⟶ x11 = x7 ⟶ x16 = x3 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x5 ⟶ x10 = x6 ⟶ x15 = x4 ⟶ x11 = x7 ⟶ x16 = x5 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ (x14 = x6 ⟶ x10 = x6 ⟶ x15 = x4 ⟶ x11 = x7 ⟶ x16 = x5 ⟶ x12 = x7 ⟶ x17 = x6 ⟶ x13 = x7 ⟶ x18) ⟶ x18
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Theorem 24237.. : ∀ 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) ⟶ (∀ x8 . x0 x8 ⟶ not (x1 x8) ⟶ ∀ x9 : ι → ο . x9 x6 ⟶ x9 x7 ⟶ x9 x8) ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x6)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x2 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x7 x9)) ⟶ ∀ x9 : ι → ι → ι → ι → ο . (∀ x10 x11 . x0 x10 ⟶ x0 x11 ⟶ x9 x10 x11 x7 x7) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x6 x7 x10) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x7 x7 x10) ⟶ x9 x2 x6 x4 x6 ⟶ x9 x2 x6 x4 x7 ⟶ x9 x2 x6 x5 x6 ⟶ x9 x2 x6 x5 x7 ⟶ x9 x2 x6 x7 x6 ⟶ x9 x2 x7 x4 x7 ⟶ x9 x2 x7 x5 x7 ⟶ x9 x3 x6 x3 x7 ⟶ x9 x3 x6 x5 x6 ⟶ x9 x3 x6 x5 x7 ⟶ x9 x3 x6 x6 x7 ⟶ x9 x3 x6 x7 x6 ⟶ x9 x3 x7 x5 x7 ⟶ x9 x4 x6 x2 x7 ⟶ x9 x4 x6 x4 x7 ⟶ x9 x5 x6 x2 x7 ⟶ x9 x5 x6 x3 x7 ⟶ x9 x6 x6 x3 x7 ⟶ x9 x7 x6 x2 x7 ⟶ x9 x7 x6 x3 x7 ⟶ x9 x7 x6 x6 x7 ⟶ (∀ x10 x11 . x0 x10 ⟶ x0 x11 ⟶ x9 x10 x11 x10 x11) ⟶ (∀ x10 x11 x12 x13 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x0 x13 ⟶ x9 x10 x11 x12 x13 ⟶ x9 x12 x13 x10 x11) ⟶ (x4 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ ∀ x16 . x0 x16 ⟶ ∀ x17 . x0 x17 ⟶ ∀ x18 . x0 x18 ⟶ ∀ x19 . x0 x19 ⟶ not (x1 x11) ⟶ not (x1 x13) ⟶ not (x1 x15) ⟶ not (x1 x17) ⟶ not (x1 x19) ⟶ x8 x10 x11 x12 x13 ⟶ x8 x12 x13 x14 x15 ⟶ x8 x14 x15 x16 x17 ⟶ x8 x16 x17 x18 x19 ⟶ not (x9 x10 x11 x12 x13) ⟶ not (x9 x10 x11 x14 x15) ⟶ not (x9 x10 x11 x16 x17) ⟶ not (x9 x10 x11 x18 x19) ⟶ not (x9 x12 x13 x14 x15) ⟶ not (x9 x12 x13 x16 x17) ⟶ not (x9 x12 x13 x18 x19) ⟶ not (x9 x14 x15 x16 x17) ⟶ not (x9 x14 x15 x18 x19) ⟶ not (x9 x16 x17 x18 x19) ⟶ ∀ x20 : ο . (x10 = x4 ⟶ x11 = x6 ⟶ x12 = x5 ⟶ x13 = x6 ⟶ x14 = x6 ⟶ x15 = x6 ⟶ x16 = x5 ⟶ x17 = x7 ⟶ x18 = x6 ⟶ x19 = x7 ⟶ x20) ⟶ (x10 = x5 ⟶ x11 = x6 ⟶ x12 = x6 ⟶ x13 = x6 ⟶ x14 = x4 ⟶ x15 = x7 ⟶ x16 = x5 ⟶ x17 = x7 ⟶ x18 = x6 ⟶ x19 = x7 ⟶ x20) ⟶ x20 (proof)
Theorem c06b6.. : ∀ 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) ⟶ (∀ x8 . x0 x8 ⟶ not (x1 x8) ⟶ ∀ x9 : ι → ο . x9 x6 ⟶ x9 x7 ⟶ x9 x8) ⟶ x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x6)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x2 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x2 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x3 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x3 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x4 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x4 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x5 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x5 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x6 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x6 x9)) ⟶ (∀ x9 . x0 x9 ⟶ not (x8 x7 x9 x7 x9)) ⟶ ∀ x9 : ι → ι → ι → ι → ο . (∀ x10 x11 . x0 x10 ⟶ x0 x11 ⟶ x9 x10 x11 x7 x7) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x6 x7 x10) ⟶ (∀ x10 . x0 x10 ⟶ x9 x6 x7 x7 x10) ⟶ x9 x2 x6 x4 x6 ⟶ x9 x2 x6 x4 x7 ⟶ x9 x2 x6 x5 x6 ⟶ x9 x2 x6 x5 x7 ⟶ x9 x2 x6 x7 x6 ⟶ x9 x2 x7 x4 x7 ⟶ x9 x2 x7 x5 x7 ⟶ x9 x3 x6 x3 x7 ⟶ x9 x3 x6 x5 x6 ⟶ x9 x3 x6 x5 x7 ⟶ x9 x3 x6 x6 x7 ⟶ x9 x3 x6 x7 x6 ⟶ x9 x3 x7 x5 x7 ⟶ x9 x4 x6 x2 x7 ⟶ x9 x4 x6 x4 x7 ⟶ x9 x5 x6 x2 x7 ⟶ x9 x5 x6 x3 x7 ⟶ x9 x6 x6 x3 x7 ⟶ x9 x7 x6 x2 x7 ⟶ x9 x7 x6 x3 x7 ⟶ x9 x7 x6 x6 x7 ⟶ (∀ x10 x11 . x0 x10 ⟶ x0 x11 ⟶ x9 x10 x11 x10 x11) ⟶ (∀ x10 x11 x12 x13 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x0 x13 ⟶ x9 x10 x11 x12 x13 ⟶ x9 x12 x13 x10 x11) ⟶ (x4 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ ∀ x16 . x0 x16 ⟶ ∀ x17 . x0 x17 ⟶ ∀ x18 . x0 x18 ⟶ ∀ x19 . x0 x19 ⟶ ∀ x20 . x0 x20 ⟶ ∀ x21 . x0 x21 ⟶ not (x1 x11) ⟶ not (x1 x13) ⟶ not (x1 x15) ⟶ not (x1 x17) ⟶ not (x1 x19) ⟶ not (x1 x21) ⟶ x8 x10 x11 x12 x13 ⟶ x8 x12 x13 x14 x15 ⟶ x8 x14 x15 x16 x17 ⟶ x8 x16 x17 x18 x19 ⟶ x8 x18 x19 x20 x21 ⟶ not (x9 x10 x11 x12 x13) ⟶ not (x9 x10 x11 x14 x15) ⟶ not (x9 x10 x11 x16 x17) ⟶ not (x9 x10 x11 x18 x19) ⟶ not (x9 x10 x11 x20 x21) ⟶ not (x9 x12 x13 x14 x15) ⟶ not (x9 x12 x13 x16 x17) ⟶ not (x9 x12 x13 x18 x19) ⟶ not (x9 x12 x13 x20 x21) ⟶ not (x9 x14 x15 x16 x17) ⟶ not (x9 x14 x15 x18 x19) ⟶ not (x9 x14 x15 x20 x21) ⟶ not (x9 x16 x17 x18 x19) ⟶ not (x9 x16 x17 x20 x21) ⟶ not (x9 x18 x19 x20 x21) ⟶ False (proof)