Proofgold Asset

Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Known ce43d.. : ∀ x0 x1 : ι → ο . ∀ x2 x3 : ι → ι → ι → ι → ο . (∀ x4 . x0 x4 ⟶ ∀ x5 . x1 x5 ⟶ ∀ x6 . x0 x6 ⟶ ∀ x7 . x0 x7 ⟶ not (x1 x7) ⟶ x2 x4 x5 x6 x7) ⟶ (∀ x4 x5 x6 x7 . x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ ∀ x8 : ο . (x2 x4 x5 x6 x7 ⟶ x8) ⟶ (x3 x4 x5 x6 x7 ⟶ x8) ⟶ (x2 x6 x7 x4 x5 ⟶ x8) ⟶ x8) ⟶ (∀ x4 x5 x6 x7 . x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x3 x4 x5 x6 x7 ⟶ x3 x6 x7 x4 x5) ⟶ ∀ x4 . x0 x4 ⟶ ∀ x5 . x0 x5 ⟶ ∀ x6 . x0 x6 ⟶ ∀ x7 . x0 x7 ⟶ ∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ x1 x5 ⟶ not (x1 x7) ⟶ not (x1 x9) ⟶ not (x1 x11) ⟶ not (x1 x13) ⟶ not (x1 x15) ⟶ not (x3 x4 x5 x6 x7) ⟶ not (x3 x4 x5 x8 x9) ⟶ not (x3 x4 x5 x10 x11) ⟶ not (x3 x4 x5 x12 x13) ⟶ not (x3 x4 x5 x14 x15) ⟶ not (x3 x6 x7 x8 x9) ⟶ not (x3 x6 x7 x10 x11) ⟶ not (x3 x6 x7 x12 x13) ⟶ not (x3 x6 x7 x14 x15) ⟶ not (x3 x8 x9 x10 x11) ⟶ not (x3 x8 x9 x12 x13) ⟶ not (x3 x8 x9 x14 x15) ⟶ not (x3 x10 x11 x12 x13) ⟶ not (x3 x10 x11 x14 x15) ⟶ not (x3 x12 x13 x14 x15) ⟶ ∀ x16 : ο . (∀ x17 . x0 x17 ⟶ ∀ x18 . x0 x18 ⟶ ∀ x19 . x0 x19 ⟶ ∀ x20 . x0 x20 ⟶ ∀ x21 . x0 x21 ⟶ ∀ x22 . x0 x22 ⟶ ∀ x23 . x0 x23 ⟶ ∀ x24 . x0 x24 ⟶ ∀ x25 . x0 x25 ⟶ ∀ x26 . x0 x26 ⟶ x2 x4 x5 x17 x18 ⟶ x2 x17 x18 x19 x20 ⟶ x2 x19 x20 x21 x22 ⟶ x2 x21 x22 x23 x24 ⟶ x2 x23 x24 x25 x26 ⟶ not (x1 x18) ⟶ not (x1 x20) ⟶ not (x1 x22) ⟶ not (x1 x24) ⟶ not (x1 x26) ⟶ not (x3 x4 x5 x17 x18) ⟶ not (x3 x4 x5 x19 x20) ⟶ not (x3 x4 x5 x21 x22) ⟶ not (x3 x4 x5 x23 x24) ⟶ not (x3 x4 x5 x25 x26) ⟶ not (x3 x17 x18 x19 x20) ⟶ not (x3 x17 x18 x21 x22) ⟶ not (x3 x17 x18 x23 x24) ⟶ not (x3 x17 x18 x25 x26) ⟶ not (x3 x19 x20 x21 x22) ⟶ not (x3 x19 x20 x23 x24) ⟶ not (x3 x19 x20 x25 x26) ⟶ not (x3 x21 x22 x23 x24) ⟶ not (x3 x21 x22 x25 x26) ⟶ not (x3 x23 x24 x25 x26) ⟶ x16) ⟶ x16
Known 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
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Theorem a83e4.. : ∀ 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 ⟶ x1 x2 ⟶ x1 x3 ⟶ x1 x4 ⟶ x1 x5 ⟶ not (x1 x6) ⟶ not (x1 x7) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x2)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x2)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x4 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x4)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x4)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x5)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x5)) ⟶ (∀ 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 x10 x11) ⟶ (∀ x10 x11 x12 x13 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x0 x13 ⟶ x9 x10 x11 x12 x13 ⟶ x9 x12 x13 x10 x11) ⟶ (∀ 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 x2 x4 x6 ⟶ x9 x2 x2 x5 x6 ⟶ x9 x3 x2 x4 x6 ⟶ x9 x3 x2 x5 x6 ⟶ x9 x4 x2 x4 x6 ⟶ x9 x4 x2 x5 x7 ⟶ x9 x4 x7 x6 x2 ⟶ x9 x5 x2 x5 x6 ⟶ x9 x6 x2 x6 x7 ⟶ 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 ⟶ (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 ⟶ not (x1 x12) ⟶ x8 x10 x2 x11 x12 ⟶ x8 x11 x12 x13 x14 ⟶ x8 x13 x14 x15 x16 ⟶ x8 x15 x16 x17 x18 ⟶ x8 x17 x18 x19 x20 ⟶ not (x9 x10 x2 x11 x12) ⟶ not (x9 x10 x2 x13 x14) ⟶ not (x9 x10 x2 x15 x16) ⟶ not (x9 x10 x2 x17 x18) ⟶ not (x9 x10 x2 x19 x20) ⟶ not (x9 x11 x12 x13 x14) ⟶ not (x9 x11 x12 x15 x16) ⟶ not (x9 x11 x12 x17 x18) ⟶ not (x9 x11 x12 x19 x20) ⟶ not (x9 x13 x14 x15 x16) ⟶ not (x9 x13 x14 x17 x18) ⟶ not (x9 x13 x14 x19 x20) ⟶ not (x9 x15 x16 x17 x18) ⟶ not (x9 x15 x16 x19 x20) ⟶ not (x9 x17 x18 x19 x20) ⟶ False (proof)
Theorem ab61b.. : ∀ 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 ⟶ x1 x2 ⟶ x1 x3 ⟶ x1 x4 ⟶ x1 x5 ⟶ not (x1 x6) ⟶ not (x1 x7) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x2)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x2)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x4 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x3)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x4)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x4)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x6 x10 x5)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ not (x8 x9 x7 x10 x5)) ⟶ (∀ 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 x10 x11) ⟶ (∀ x10 x11 x12 x13 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x0 x13 ⟶ x9 x10 x11 x12 x13 ⟶ x9 x12 x13 x10 x11) ⟶ (∀ 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 x2 x4 x6 ⟶ x9 x2 x2 x5 x6 ⟶ x9 x3 x2 x4 x6 ⟶ x9 x3 x2 x5 x6 ⟶ x9 x4 x2 x4 x6 ⟶ x9 x4 x2 x5 x7 ⟶ x9 x4 x7 x6 x2 ⟶ x9 x5 x2 x5 x6 ⟶ x9 x6 x2 x6 x7 ⟶ 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 ⟶ (x4 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (∀ x10 : ι → ο . x10 x2 ⟶ x10 x3 ⟶ x10 x4 ⟶ x10 x5 ⟶ ∀ x11 . x1 x11 ⟶ x10 x11) ⟶ (∀ x10 . x0 x10 ⟶ ∀ x11 . x1 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x1 x13) ⟶ x8 x10 x11 x12 x13) ⟶ (∀ x10 x11 x12 x13 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x0 x13 ⟶ ∀ x14 : ο . (x8 x10 x11 x12 x13 ⟶ x14) ⟶ (x9 x10 x11 x12 x13 ⟶ x14) ⟶ (x8 x12 x13 x10 x11 ⟶ x14) ⟶ x14) ⟶ ∀ x10 x11 x12 : ι → ι → ι . (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x0 (x10 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x1 x14 ⟶ x1 (x10 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x10 x13 (x10 x13 x14) = x14) ⟶ (∀ x13 . x0 x13 ⟶ x10 x13 x2 = x3) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x0 (x11 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x1 x14 ⟶ x1 (x11 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x11 x13 (x11 x13 x14) = x14) ⟶ (∀ x13 . x0 x13 ⟶ x11 x13 x2 = x4) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x0 (x12 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x1 x14 ⟶ x1 (x12 x13 x14)) ⟶ (∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ x12 x13 (x12 x13 x14) = x14) ⟶ (∀ x13 . x0 x13 ⟶ x12 x13 x2 = x5) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x9 x13 x14 x15 x16) ⟶ not (x9 x13 (x10 x13 x14) x15 (x10 x15 x16))) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x9 x13 x14 x15 x16) ⟶ not (x9 x13 (x11 x13 x14) x15 (x11 x15 x16))) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x9 x13 x14 x15 x16) ⟶ not (x9 x13 (x12 x13 x14) x15 (x12 x15 x16))) ⟶ ∀ x13 . x1 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 ⟶ ∀ x22 . x0 x22 ⟶ ∀ x23 . x0 x23 ⟶ ∀ x24 . x0 x24 ⟶ not (x1 x16) ⟶ x8 x14 x13 x15 x16 ⟶ x8 x15 x16 x17 x18 ⟶ x8 x17 x18 x19 x20 ⟶ x8 x19 x20 x21 x22 ⟶ x8 x21 x22 x23 x24 ⟶ not (x9 x14 x13 x15 x16) ⟶ not (x9 x14 x13 x17 x18) ⟶ not (x9 x14 x13 x19 x20) ⟶ not (x9 x14 x13 x21 x22) ⟶ not (x9 x14 x13 x23 x24) ⟶ not (x9 x15 x16 x17 x18) ⟶ not (x9 x15 x16 x19 x20) ⟶ not (x9 x15 x16 x21 x22) ⟶ not (x9 x15 x16 x23 x24) ⟶ not (x9 x17 x18 x19 x20) ⟶ not (x9 x17 x18 x21 x22) ⟶ not (x9 x17 x18 x23 x24) ⟶ not (x9 x19 x20 x21 x22) ⟶ not (x9 x19 x20 x23 x24) ⟶ not (x9 x21 x22 x23 x24) ⟶ False (proof)