Proofgold Address

Param ap^ap : ι → ι → ι
Param not^not : ο → ο
Definition False^False := ∀ x0 : ο . x0
Known 3c6b1.. : ∀ x0 : ι → ο . ∀ x1 x2 x3 x4 x5 x6 . x0 x1 ⟶ ∀ x7 : ι → ι . (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ x0 (ap (x7 x8) x9)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ ap (x7 x8) (ap (x7 x8) x9) = x9) ⟶ (∀ x8 . x0 x8 ⟶ ap (x7 x8) x1 = x2) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x9 (ap (x7 x9) x10) x11 (ap (x7 x11) x12)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x1 x10 x11) ⟶ not (x8 x9 x1 x12 x13) ⟶ not (x8 x9 x1 x14 x15) ⟶ not (x8 x9 x1 x16 x17) ⟶ not (x8 x9 x1 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False) ⟶ ∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x2 x10 x11) ⟶ not (x8 x9 x2 x12 x13) ⟶ not (x8 x9 x2 x14 x15) ⟶ not (x8 x9 x2 x16 x17) ⟶ not (x8 x9 x2 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False
Known f8a5d.. : ∀ x0 : ι → ο . ∀ x1 x2 x3 x4 x5 x6 . x0 x1 ⟶ ∀ x7 : ι → ι . (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ x0 (ap (x7 x8) x9)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ ap (x7 x8) (ap (x7 x8) x9) = x9) ⟶ (∀ x8 . x0 x8 ⟶ ap (x7 x8) x1 = x3) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x9 (ap (x7 x9) x10) x11 (ap (x7 x11) x12)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x1 x10 x11) ⟶ not (x8 x9 x1 x12 x13) ⟶ not (x8 x9 x1 x14 x15) ⟶ not (x8 x9 x1 x16 x17) ⟶ not (x8 x9 x1 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False) ⟶ ∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x3 x10 x11) ⟶ not (x8 x9 x3 x12 x13) ⟶ not (x8 x9 x3 x14 x15) ⟶ not (x8 x9 x3 x16 x17) ⟶ not (x8 x9 x3 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False
Known 37836.. : ∀ x0 : ι → ο . ∀ x1 x2 x3 x4 x5 x6 . x0 x1 ⟶ ∀ x7 : ι → ι . (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ x0 (ap (x7 x8) x9)) ⟶ (∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ ap (x7 x8) (ap (x7 x8) x9) = x9) ⟶ (∀ x8 . x0 x8 ⟶ ap (x7 x8) x1 = x4) ⟶ ∀ x8 : ι → ι → ι → ι → ο . (∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x9 (ap (x7 x9) x10) x11 (ap (x7 x11) x12)) ⟶ (∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x1 x10 x11) ⟶ not (x8 x9 x1 x12 x13) ⟶ not (x8 x9 x1 x14 x15) ⟶ not (x8 x9 x1 x16 x17) ⟶ not (x8 x9 x1 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False) ⟶ ∀ x9 . x0 x9 ⟶ ∀ 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 (x8 x9 x4 x10 x11) ⟶ not (x8 x9 x4 x12 x13) ⟶ not (x8 x9 x4 x14 x15) ⟶ not (x8 x9 x4 x16 x17) ⟶ not (x8 x9 x4 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False
Theorem 54331.. : ∀ x0 x1 : ι → ο . ∀ x2 x3 x4 x5 x6 x7 . (∀ x8 : ι → ο . x8 x2 ⟶ x8 x3 ⟶ x8 x4 ⟶ x8 x5 ⟶ ∀ x9 . x1 x9 ⟶ x8 x9) ⟶ x0 x2 ⟶ ∀ x8 x9 x10 : ι → ι . (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x8 x11) x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x8 x11) (ap (x8 x11) x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ ap (x8 x11) x2 = x3) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x9 x11) x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x9 x11) (ap (x9 x11) x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ ap (x9 x11) x2 = x4) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x10 x11) x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x10 x11) (ap (x10 x11) x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ ap (x10 x11) x2 = x5) ⟶ ∀ x11 : ι → ι → ι → ι → ο . (∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x8 x12) x13) x14 (ap (x8 x14) x15)) ⟶ (∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x9 x12) x13) x14 (ap (x9 x14) x15)) ⟶ (∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x10 x12) x13) x14 (ap (x10 x14) x15)) ⟶ (∀ 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 ⟶ ∀ x22 . x0 x22 ⟶ not (x11 x12 x2 x13 x14) ⟶ not (x11 x12 x2 x15 x16) ⟶ not (x11 x12 x2 x17 x18) ⟶ not (x11 x12 x2 x19 x20) ⟶ not (x11 x12 x2 x21 x22) ⟶ not (x11 x13 x14 x15 x16) ⟶ not (x11 x13 x14 x17 x18) ⟶ not (x11 x13 x14 x19 x20) ⟶ not (x11 x13 x14 x21 x22) ⟶ not (x11 x15 x16 x17 x18) ⟶ not (x11 x15 x16 x19 x20) ⟶ not (x11 x15 x16 x21 x22) ⟶ not (x11 x17 x18 x19 x20) ⟶ not (x11 x17 x18 x21 x22) ⟶ not (x11 x19 x20 x21 x22) ⟶ False) ⟶ ∀ 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 ⟶ ∀ x22 . x0 x22 ⟶ ∀ x23 . x1 x23 ⟶ not (x11 x12 x23 x13 x14) ⟶ not (x11 x12 x23 x15 x16) ⟶ not (x11 x12 x23 x17 x18) ⟶ not (x11 x12 x23 x19 x20) ⟶ not (x11 x12 x23 x21 x22) ⟶ not (x11 x13 x14 x15 x16) ⟶ not (x11 x13 x14 x17 x18) ⟶ not (x11 x13 x14 x19 x20) ⟶ not (x11 x13 x14 x21 x22) ⟶ not (x11 x15 x16 x17 x18) ⟶ not (x11 x15 x16 x19 x20) ⟶ not (x11 x15 x16 x21 x22) ⟶ not (x11 x17 x18 x19 x20) ⟶ not (x11 x17 x18 x21 x22) ⟶ not (x11 x19 x20 x21 x22) ⟶ False (proof)