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Proofgold Signed Transaction

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PrQyi../1345f..
PUQqQ../ef684..
vout
PrQyi../5add9.. 6.17 bars
TMFqP../2b555.. ownership of 27109.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMJRL../aa65a.. ownership of 65dff.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
PUVBP../fb602.. doc published by Pr4zB..
Definition Church13_p := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x7) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x8) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x9) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x10) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x11) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x12) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x13) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x14) ⟶ x1 x0
Definition TwoRamseyGraph_3_5_Church13 := λ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x2 x3 . x0 (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x2) (x1 x2 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3) (x1 x3 x2 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3) (x1 x3 x3 x2 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3) (x1 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x3 x3 x2) (x1 x2 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x3 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x3) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2) (x1 x2 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x3) (x1 x3 x2 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3) (x1 x3 x3 x2 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3) (x1 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x2 x3 x2) (x1 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x2 x3)
Definition FalseFalse := ∀ x0 : ο . x0
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Known 768c1.. : ((λ x1 x2 . x2) = λ x1 x2 . x1) ⟶ ∀ x0 : ο . x0
Theorem 27109.. : ∀ x0 x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church13_p x0 ⟶ Church13_p x1 ⟶ Church13_p x2 ⟶ (((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x0 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x1 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x2 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) = x0 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) = x1 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) = x2 ⟶ ∀ x3 : ο . x3) ⟶ (x0 = x1 ⟶ ∀ x3 : ο . x3) ⟶ (x0 = x2 ⟶ ∀ x3 : ο . x3) ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x0 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) x0 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x0 x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x0 x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x1 x2 = λ x4 x5 . x5) ⟶ False (proof)