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Proofgold Signed Transaction

vin
PrCit../66f97..
PUcMB../55c2d..
vout
PrCit../657ff.. 4.98 bars
TMRhp../0a76c.. ownership of ca0b4.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMT5w../d194d.. ownership of 1de52.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMPZc../8dd0d.. ownership of 82851.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMXN7../8dff5.. ownership of ac637.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMZBc../264a2.. ownership of cf7fd.. as obj with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMc9x../ec7f3.. ownership of dabe1.. as obj with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
PUZeT../335db.. doc published by Pr4zB..
Definition Church17_lt8 := λ x0 : ι → ι → ι → ι → 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 → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9) ⟶ x1 x0
Definition TwoRamseyGraph_3_6_Church17 := λ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x2 x3 . x0 (x1 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x3 x2 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x2 x2 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x3 x2 x3 x3 x2 x3 x2 x2 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x2 x3 x3 x3 x3 x2 x2 x2 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x2 x2 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x2 x2 x3 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x2 x3 x3 x2 x2 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x2 x3 x3 x2 x3 x3 x3 x2) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x2) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x3 x2 x3 x2) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x2) (x1 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x2 x2 x2 x2 x2)
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 82851.. : ∀ x0 x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_lt8 x0 ⟶ Church17_lt8 x1 ⟶ Church17_lt8 x2 ⟶ (TwoRamseyGraph_3_6_Church17 x0 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x13) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x13) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x13) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 x2 = λ x4 x5 . x5) ⟶ False (proof)
Theorem ca0b4.. : ∀ x0 x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_lt8 x0 ⟶ Church17_lt8 x1 ⟶ Church17_lt8 x2 ⟶ (TwoRamseyGraph_3_6_Church17 x0 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x14) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x14) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x12) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x14) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 x2 = λ x4 x5 . x5) ⟶ False (proof)