Proofgold Proposition

∀ 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 : ι → ο . x8 x2 ⟶ x8 x3 ⟶ x8 x4 ⟶ x8 x5 ⟶ ∀ x9 . x1 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) ⟶ (x2 = x3 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x6 = x7 ⟶ ∀ x8 : ο . x8) ⟶ ∀ x8 x9 x10 : ι → ι → ι . (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (x8 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x1 x12 ⟶ x1 (x8 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x8 x11 (x8 x11 x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ x8 x11 x2 = x3) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (x9 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x1 x12 ⟶ x1 (x9 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x9 x11 (x9 x11 x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ x9 x11 x2 = x4) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (x10 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x1 x12 ⟶ x1 (x10 x11 x12)) ⟶ (∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x10 x11 (x10 x11 x12) = x12) ⟶ (∀ x11 . x0 x11 ⟶ x10 x11 x2 = x5) ⟶ ∀ x11 : ι → ι → ι → ι → ο . (∀ x12 x13 . not (x11 x12 x13 x12 x13)) ⟶ (∀ x12 x13 x14 x15 x16 x17 . x0 x16 ⟶ x0 x17 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x14 x15 x16 x17 ⟶ x11 x12 x13 x16 x17) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x1 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ not (x1 x15) ⟶ x11 x12 x13 x14 x15) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x3 x13 x2)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x4 x13 x2)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x5 x13 x2)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x6 x13 x2)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x2)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x4 x13 x3)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x5 x13 x3)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x6 x13 x3)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x3)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x5 x13 x4)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x6 x13 x4)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x4)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x6 x13 x5)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x5)) ⟶ (∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x6)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x2 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x3 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x4 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x2 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x3 x12 x3 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x4 x12 x3 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x12 x3 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x12 x3 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x3 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x4 x12 x4 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x12 x4 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x12 x4 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x4 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x5 x12 x5 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x12 x5 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x5 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x6 x12 x6 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x6 x12)) ⟶ (∀ x12 . x0 x12 ⟶ not (x11 x7 x12 x7 x12)) ⟶ ∀ x12 : ι → ι → ι → ι → ο . (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ ∀ x17 : ο . (x11 x13 x14 x15 x16 ⟶ x17) ⟶ (x12 x13 x14 x15 x16 ⟶ x17) ⟶ (x11 x15 x16 x13 x14 ⟶ x17) ⟶ x17) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x12 x13 x14 x15 x16) ⟶ not (x12 x13 (x8 x13 x14) x15 (x8 x15 x16))) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x12 x13 x14 x15 x16) ⟶ not (x12 x13 (x9 x13 x14) x15 (x9 x15 x16))) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ not (x12 x13 x14 x15 x16) ⟶ not (x12 x13 (x10 x13 x14) x15 (x10 x15 x16))) ⟶ (∀ x13 x14 . x0 x13 ⟶ x0 x14 ⟶ x12 x13 x14 x13 x14) ⟶ (∀ x13 x14 x15 x16 . x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x0 x16 ⟶ x12 x13 x14 x15 x16 ⟶ x12 x15 x16 x13 x14) ⟶ (∀ x13 x14 . x0 x13 ⟶ x0 x14 ⟶ x12 x13 x14 x7 x7) ⟶ (∀ x13 . x0 x13 ⟶ x12 x6 x6 x7 x13) ⟶ (∀ x13 . x0 x13 ⟶ x12 x6 x7 x7 x13) ⟶ x12 x2 x2 x2 x4 ⟶ x12 x2 x2 x2 x6 ⟶ x12 x2 x2 x3 x2 ⟶ x12 x2 x2 x3 x3 ⟶ x12 x2 x2 x3 x6 ⟶ x12 x2 x2 x4 x4 ⟶ x12 x2 x2 x4 x5 ⟶ x12 x2 x2 x4 x6 ⟶ x12 x2 x2 x5 x3 ⟶ x12 x2 x2 x5 x4 ⟶ x12 x2 x2 x5 x6 ⟶ x12 x2 x2 x6 x4 ⟶ x12 x2 x2 x6 x5 ⟶ x12 x2 x2 x7 x2 ⟶ x12 x2 x2 x7 x4 ⟶ x12 x2 x2 x7 x5 ⟶ x12 x2 x3 x2 x5 ⟶ x12 x2 x3 x2 x7 ⟶ x12 x2 x3 x3 x2 ⟶ x12 x2 x3 x3 x3 ⟶ x12 x2 x3 x3 x7 ⟶ x12 x2 x3 x4 x4 ⟶ x12 x2 x3 x4 x5 ⟶ x12 x2 x3 x4 x7 ⟶ x12 x2 x3 x5 x2 ⟶ x12 x2 x3 x5 x5 ⟶ x12 x2 x3 x5 x7 ⟶ x12 x2 x3 x6 x4 ⟶ x12 x2 x3 x6 x5 ⟶ x12 x2 x3 x7 x3 ⟶ x12 x2 x3 x7 x4 ⟶ x12 x2 x3 x7 x5 ⟶ x12 x2 x4 x2 x7 ⟶ x12 x2 x4 x3 x4 ⟶ x12 x2 x4 x3 x5 ⟶ x12 x2 x4 x3 x6 ⟶ x12 x2 x4 x4 x2 ⟶ x12 x2 x4 x4 x3 ⟶ x12 x2 x4 x4 x6 ⟶ x12 x2 x4 x5 x2 ⟶ x12 x2 x4 x5 x5 ⟶ x12 x2 x4 x5 x7 ⟶ x12 x2 x4 x6 x2 ⟶ x12 x2 x4 x6 x3 ⟶ x12 x2 x4 x7 x2 ⟶ x12 x2 x4 x7 x3 ⟶ x12 x2 x4 x7 x4 ⟶ x12 x2 x5 x2 x6 ⟶ x12 x2 x5 x3 x4 ⟶ x12 x2 x5 x3 x5 ⟶ x12 x2 x5 x3 x7 ⟶ x12 x2 x5 x4 x2 ⟶ x12 x2 x5 x4 x3 ⟶ x12 x2 x5 x4 x7 ⟶ x12 x2 x5 x5 x3 ⟶ x12 x2 x5 x5 x4 ⟶ x12 x2 x5 x5 x6 ⟶ x12 x2 x5 x6 x2 ⟶ x12 x2 x5 x6 x3 ⟶ x12 x2 x5 x7 x2 ⟶ x12 x2 x5 x7 x3 ⟶ x12 x2 x5 x7 x5 ⟶ x12 x2 x6 x3 x3 ⟶ x12 x2 x6 x3 x4 ⟶ x12 x2 x6 x4 x2 ⟶ x12 x2 x6 x4 x5 ⟶ x12 x2 x6 x4 x6 ⟶ x12 x2 x6 x4 x7 ⟶ x12 x2 x6 x5 x2 ⟶ x12 x2 x6 x5 x5 ⟶ x12 x2 x6 x5 x6 ⟶ x12 x2 x6 x5 x7 ⟶ x12 x2 x6 x6 x3 ⟶ x12 x2 x6 x6 x4 ⟶ x12 x2 x6 x7 x6 ⟶ x12 x2 x7 x3 x2 ⟶ x12 x2 x7 x3 x5 ⟶ x12 x2 x7 x4 x3 ⟶ x12 x2 x7 x4 x4 ⟶ x12 x2 x7 x4 x6 ⟶ x12 x2 x7 x4 x7 ⟶ x12 x2 x7 x5 x3 ⟶ x12 x2 x7 x5 x4 ⟶ x12 x2 x7 x5 x6 ⟶ x12 x2 x7 x5 x7 ⟶ x12 x2 x7 x6 x2 ⟶ x12 x2 x7 x6 x5 ⟶ x12 x2 x7 x7 x6 ⟶ x12 x3 x2 x3 x4 ⟶ x12 x3 x2 x3 x7 ⟶ x12 x3 x2 x4 x2 ⟶ x12 x3 x2 x4 x6 ⟶ x12 x3 x2 x5 x3 ⟶ x12 x3 x2 x5 x4 ⟶ x12 x3 x2 x5 x5 ⟶ x12 x3 x2 x5 x6 ⟶ x12 x3 x2 x6 x3 ⟶ x12 x3 x2 x6 x4 ⟶ x12 x3 x2 x6 x7 ⟶ x12 x3 x2 x7 x3 ⟶ x12 x3 x3 x3 x5 ⟶ x12 x3 x3 x3 x6 ⟶ x12 x3 x3 x4 x3 ⟶ x12 x3 x3 x4 x7 ⟶ x12 x3 x3 x5 x2 ⟶ x12 x3 x3 x5 x4 ⟶ x12 x3 x3 x5 x5 ⟶ x12 x3 x3 x5 x7 ⟶ x12 x3 x3 x6 x2 ⟶ x12 x3 x3 x6 x5 ⟶ x12 x3 x3 x6 x6 ⟶ x12 x3 x3 x7 x2 ⟶ x12 x3 x4 x3 x7 ⟶ x12 x3 x4 x4 x4 ⟶ x12 x3 x4 x4 x6 ⟶ x12 x3 x4 x5 x2 ⟶ x12 x3 x4 x5 x3 ⟶ x12 x3 x4 x5 x5 ⟶ x12 x3 x4 x5 x7 ⟶ x12 x3 x4 x6 x2 ⟶ x12 x3 x4 x6 x5 ⟶ x12 x3 x4 x6 x7 ⟶ x12 x3 x4 x7 x5 ⟶ x12 x3 x5 x3 x6 ⟶ x12 x3 x5 x4 x5 ⟶ x12 x3 x5 x4 x7 ⟶ x12 x3 x5 x5 x2 ⟶ x12 x3 x5 x5 x3 ⟶ x12 x3 x5 x5 x4 ⟶ x12 x3 x5 x5 x6 ⟶ x12 x3 x5 x6 x3 ⟶ x12 x3 x5 x6 x4 ⟶ x12 x3 x5 x6 x6 ⟶ x12 x3 x5 x7 x4 ⟶ x12 x3 x6 x3 x7 ⟶ x12 x3 x6 x4 x3 ⟶ x12 x3 x6 x4 x5 ⟶ x12 x3 x6 x5 x6 ⟶ x12 x3 x6 x5 x7 ⟶ x12 x3 x6 x6 x7 ⟶ x12 x3 x6 x7 x3 ⟶ x12 x3 x6 x7 x5 ⟶ x12 x3 x6 x7 x6 ⟶ x12 x3 x7 x4 x2 ⟶ x12 x3 x7 x4 x4 ⟶ x12 x3 x7 x5 x6 ⟶ x12 x3 x7 x5 x7 ⟶ x12 x3 x7 x6 x6 ⟶ x12 x3 x7 x7 x2 ⟶ x12 x3 x7 x7 x4 ⟶ x12 x3 x7 x7 x6 ⟶ x12 x4 x2 x4 x3 ⟶ x12 x4 x2 x4 x6 ⟶ x12 x4 x2 x5 x3 ⟶ x12 x4 x2 x5 x4 ⟶ x12 x4 x2 x5 x7 ⟶ x12 x4 x2 x6 x4 ⟶ x12 x4 x2 x6 x5 ⟶ x12 x4 x2 x7 x4 ⟶ x12 x4 x2 x7 x6 ⟶ x12 x4 x3 x4 x7 ⟶ x12 x4 x3 x5 x2 ⟶ x12 x4 x3 x5 x5 ⟶ x12 x4 x3 x5 x6 ⟶ x12 x4 x3 x6 x4 ⟶ x12 x4 x3 x6 x5 ⟶ x12 x4 x3 x7 x5 ⟶ x12 x4 x3 x7 x6 ⟶ x12 x4 x4 x4 x5 ⟶ x12 x4 x4 x4 x6 ⟶ x12 x4 x4 x5 x2 ⟶ x12 x4 x4 x5 x5 ⟶ x12 x4 x4 x5 x6 ⟶ x12 x4 x4 x6 x2 ⟶ x12 x4 x4 x6 x3 ⟶ x12 x4 x4 x7 x2 ⟶ x12 x4 x4 x7 x6 ⟶ x12 x4 x5 x4 x7 ⟶ x12 x4 x5 x5 x3 ⟶ x12 x4 x5 x5 x4 ⟶ x12 x4 x5 x5 x7 ⟶ x12 x4 x5 x6 x2 ⟶ x12 x4 x5 x6 x3 ⟶ x12 x4 x5 x7 x3 ⟶ x12 x4 x5 x7 x6 ⟶ x12 x4 x6 x2 x7 ⟶ x12 x4 x6 x4 x7 ⟶ x12 x4 x6 x6 x3 ⟶ x12 x4 x6 x6 x5 ⟶ x12 x4 x7 x6 x2 ⟶ x12 x4 x7 x6 x4 ⟶ x12 x5 x2 x5 x3 ⟶ x12 x5 x2 x5 x6 ⟶ x12 x5 x2 x6 x4 ⟶ x12 x5 x2 x6 x7 ⟶ x12 x5 x2 x7 x2 ⟶ x12 x5 x2 x7 x3 ⟶ x12 x5 x2 x7 x6 ⟶ x12 x5 x3 x5 x7 ⟶ x12 x5 x3 x6 x5 ⟶ x12 x5 x3 x6 x6 ⟶ x12 x5 x3 x7 x2 ⟶ x12 x5 x3 x7 x3 ⟶ x12 x5 x3 x7 x6 ⟶ x12 x5 x4 x5 x5 ⟶ x12 x5 x4 x5 x7 ⟶ x12 x5 x4 x6 x2 ⟶ x12 x5 x4 x6 x7 ⟶ x12 x5 x4 x7 x4 ⟶ x12 x5 x4 x7 x5 ⟶ x12 x5 x4 x7 x6 ⟶ x12 x5 x5 x5 x6 ⟶ x12 x5 x5 x6 x3 ⟶ x12 x5 x5 x6 x6 ⟶ x12 x5 x5 x7 x4 ⟶ x12 x5 x5 x7 x5 ⟶ x12 x5 x5 x7 x6 ⟶ x12 x5 x6 x2 x7 ⟶ x12 x5 x6 x3 x7 ⟶ x12 x5 x6 x7 x3 ⟶ x12 x5 x6 x7 x4 ⟶ x12 x5 x7 x7 x2 ⟶ x12 x5 x7 x7 x5 ⟶ x12 x6 x2 x6 x4 ⟶ x12 x6 x2 x6 x5 ⟶ x12 x6 x2 x6 x7 ⟶ x12 x6 x2 x7 x2 ⟶ x12 x6 x2 x7 x3 ⟶ x12 x6 x3 x6 x4 ⟶ x12 x6 x3 x6 x5 ⟶ x12 x6 x3 x6 x6 ⟶ x12 x6 x3 x7 x2 ⟶ x12 x6 x3 x7 x3 ⟶ x12 x6 x4 x6 x7 ⟶ x12 x6 x4 x7 x4 ⟶ x12 x6 x4 x7 x5 ⟶ x12 x6 x5 x6 x6 ⟶ x12 x6 x5 x7 x4 ⟶ x12 x6 x5 x7 x5 ⟶ x12 x6 x6 x3 x7 ⟶ x12 x7 x2 x7 x5 ⟶ x12 x7 x3 x7 x4 ⟶ x12 x7 x6 x2 x7 ⟶ x12 x7 x6 x3 x7 ⟶ x12 x7 x6 x6 x7 ⟶ ∀ 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 ⟶ x11 x2 x2 x13 x3 ⟶ x11 x13 x3 x14 x15 ⟶ x11 x14 x15 x16 x17 ⟶ x11 x16 x17 x18 x19 ⟶ x11 x18 x19 x20 x21 ⟶ not (x12 x2 x2 x13 x3) ⟶ not (x12 x2 x2 x14 x15) ⟶ not (x12 x2 x2 x16 x17) ⟶ not (x12 x2 x2 x18 x19) ⟶ not (x12 x2 x2 x20 x21) ⟶ not (x12 x13 x3 x14 x15) ⟶ not (x12 x13 x3 x16 x17) ⟶ not (x12 x13 x3 x18 x19) ⟶ not (x12 x13 x3 x20 x21) ⟶ not (x12 x14 x15 x16 x17) ⟶ not (x12 x14 x15 x18 x19) ⟶ not (x12 x14 x15 x20 x21) ⟶ not (x12 x16 x17 x18 x19) ⟶ not (x12 x16 x17 x20 x21) ⟶ not (x12 x18 x19 x20 x21) ⟶ False

type
prop

theory
HotG

name
-

proof
PUbUo..

Megalodon
-

proofgold address
TMY98..

creator
21762 Pr4zB../53098..

owner
21762 Pr4zB../53098..

term root
d2c3c..