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Proofgold Signed Transaction

vin
PrPhD../bb608..
PUZ4p../02ede..
vout
PrPhD../cd61f.. 3.40 bars
TMV3s../4f275.. ownership of c7cce.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
TML8Z../e4b4d.. ownership of 09b3b.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
PUPtD../e2d5b.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem c7cce.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . ∀ x8 : ι → ο . ∀ x9 x10 x11 : ι → ι . ∀ x12 : ι → ο . ∀ x13 x14 : ι → ι . ∀ x15 . ∀ x16 : ι → ι → ο . ∀ x17 x18 : ι → ο . ∀ x19 x20 : ι → ι → ι . ∀ x21 : ι → ι . ∀ x22 x23 x24 x25 . ∀ x26 : ι → ι → ο . ∀ x27 x28 . ∀ x29 x30 : ι → ι . ∀ x31 : ι → ο . ∀ x32 : ι → ι → ι . ∀ x33 : ι → ι → ο . ∀ x34 : ι → ι . ∀ x35 x36 . ∀ x37 : ι → ι . ∀ x38 : ι → ο . ∀ x39 : ι → ι . ∀ x40 : ι → ι → ο . ∀ x41 : ι → ι . ∀ x42 : ι → ι → ι . ∀ x43 x44 : ι → ι . ∀ x45 : ι → ο . ∀ x46 : ι → ι → ι → ι → ι . ∀ x47 : ι → ι → ι . ∀ x48 x49 : ι → ι → ι → ο . ∀ x50 : ι → ι → ι . ∀ x51 x52 : ι → ι → ι → ι . ∀ x53 : ι → ο . ∀ x54 : ι → ι → ο . ∀ x55 : ι → ι . ∀ x56 : ι → ι → ι → ι . ∀ x57 : ι → ι → ι . ∀ x58 : ι → ι → ι → ι . ∀ x59 x60 : ι → ο . ∀ x61 . ∀ x62 : ι → ο . (∀ x63 x64 . x62 x64(x64 = x63False)x62 x63False)(∀ x63 x64 . x0 x63 x64x62 x64False)(∀ x63 . x62 x63(x63 = x61False)False)(∀ x63 x64 x65 . x0 x63 x64x2 x64 (x1 x65)x62 x65False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x57 x65 (x58 x65 x63 x64) = x56 (x55 x65) (x57 x65 x63) (x57 x65 x64)False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x3 x65 (x58 x65 x63 x64) = x56 (x55 x65) (x3 x65 x63) (x3 x65 x64)False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x57 x65 (x52 x65 x63 x64) = x51 (x55 x65) (x57 x65 x63) (x57 x65 x64)False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x3 x65 (x52 x65 x63 x64) = x51 (x55 x65) (x3 x65 x63) (x3 x65 x64)False)False)(∀ x63 x64 x65 . x0 x64 x65x2 x65 (x1 x63)(x2 x64 x63False)False)(∀ x63 x64 . x4 x64 x63(x2 x64 (x1 x63)False)False)(∀ x63 x64 . x2 x64 (x1 x63)(x4 x64 x63False)False)(∀ x63 x64 . x2 x63 x64(x62 x64False)(x0 x63 x64False)False)(∀ x63 . (x50 x63 x61 = x61False)False)(∀ x63 x64 . (x5 x63 (x50 x63 x64) = x63False)False)(∀ x63 x64 . x0 x64 x63(x2 x64 x63False)False)(∀ x63 . (x5 x63 x61 = x63False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x49 x65 x63 x64(x49 x65 x64 x63False)False)(x62 x6False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x49 x65 x63 x63False)False)(∀ x63 . (x4 x63 x63False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x63 = x64(x49 x65 x63 x64False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x49 x65 x63 x64(x63 = x64False)False)(∀ x63 x64 x65 . (x62 x65False)(x62 x63False)x2 x63 (x1 x65)x2 x64 x63(x48 x64 x65 x63False)False)(∀ x63 x64 x65 . (x62 x65False)(x62 x63False)x2 x63 (x1 x65)x48 x64 x65 x63(x2 x64 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)(x56 x65 x63 x64 = x50 x63 x64False)False)(∀ x63 . (x7 x63 = x1 x63False)False)(∀ x63 x64 x65 x66 . x2 x65 (x1 x66)x2 x64 (x1 x63)(x46 x66 x63 x65 x64 = x47 x65 x64False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x51 x65 x64 x63 = x5 x64 x63False)False)(∀ x63 . x45 x63(x42 (x43 x63) (x44 x63) = x63False)False)(∀ x63 x64 . (x44 (x42 x64 x63) = x63False)False)(∀ x63 x64 . (x43 (x42 x63 x64) = x63False)False)(∀ x63 . (x8 x63False)x8 (x9 x63)False)(∀ x63 . (x8 x63False)(x2 (x9 x63) (x1 x63)False)False)(∀ x63 . (x62 x63False)(x8 (x10 x63)False)False)(∀ x63 . (x62 x63False)x62 (x10 x63)False)(∀ x63 . (x62 x63False)(x2 (x10 x63) (x1 x63)False)False)(∀ x63 . (x62 x63False)(x40 (x41 x63) x63False)False)(∀ x63 . (x62 x63False)(x2 (x41 x63) (x1 x63)False)False)(∀ x63 . (x60 x63False)x38 x63x62 (x39 x63)False)(∀ x63 . (x60 x63False)x38 x63(x2 (x39 x63) (x1 (x55 x63))False)False)(∀ x63 . x40 (x37 x63) x63False)(∀ x63 . (x2 (x37 x63) (x1 x63)False)False)(x62 x36False)(∀ x63 . (x62 (x11 x63)False)False)(∀ x63 . (x2 (x11 x63) (x1 x63)False)False)(∀ x63 . (x12 x63False)x38 x63x8 (x13 x63)False)(∀ x63 . (x12 x63False)x38 x63(x2 (x13 x63) (x1 (x55 x63))False)False)(∀ x63 . (x60 x63False)x38 x63(x8 (x14 x63)False)False)(∀ x63 . (x60 x63False)x38 x63x62 (x14 x63)False)(∀ x63 . (x60 x63False)x38 x63(x2 (x14 x63) (x1 (x55 x63))False)False)((x45 x35False)False)((x62 x15False)False)(∀ x63 . (x62 x63False)x62 (x34 x63)False)(∀ x63 . (x62 x63False)(x2 (x34 x63) (x1 x63)False)False)(∀ x63 x64 . (x33 (x32 x63 x64) x63False)False)(∀ x63 x64 . (x16 (x32 x64 x63) x63False)False)(∀ x63 x64 . (x31 (x32 x63 x64)False)False)(∀ x63 x64 . (x62 (x32 x63 x64)False)False)(∀ x63 x64 . (x2 (x32 x63 x64) (x1 (x47 x64 x63))False)False)(∀ x63 x64 x65 . x2 x63 (x1 x65)(x56 x65 x64 x64 = x64False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x51 x65 x64 x64 = x64False)False)(∀ x63 . (x50 x63 x63 = x63False)False)(∀ x63 . (x5 x63 x63 = x63False)False)(∀ x63 . (x17 x63False)x38 x63x18 (x55 x63)False)(∀ x63 . x17 x63x38 x63(x18 (x55 x63)False)False)(∀ x63 . x12 x63x38 x63(x8 (x55 x63)False)False)(∀ x63 . (x12 x63False)x38 x63x8 (x55 x63)False)(∀ x63 x64 . (x62 x64False)x62 (x5 x63 x64)False)(∀ x63 x64 x65 . x31 x65x33 x65 x63x31 x64(x33 (x50 x65 x64) x63False)False)(∀ x63 x64 . (x62 x64False)x62 (x5 x64 x63)False)(∀ x63 x64 x65 . x31 x65x33 x65 x63x31 x64x33 x64 x63(x33 (x5 x65 x64) x63False)False)(∀ x63 x64 . x62 (x19 x63 x64)False)(∀ x63 . x62 (x30 x63)False)(∀ x63 . (x60 x63False)x38 x63x62 (x55 x63)False)(∀ x63 x64 x65 . x31 x65x16 x65 x63x31 x64(x16 (x50 x65 x64) x63False)False)(∀ x63 x64 . (x45 (x42 x63 x64)False)False)((x62 x61False)False)(∀ x63 . x62 (x1 x63)False)(∀ x63 . x60 x63x38 x63(x62 (x55 x63)False)False)(∀ x63 x64 x65 . x31 x65x16 x65 x63x31 x64x16 x64 x63(x16 (x5 x65 x64) x63False)False)(∀ x63 x64 . (x62 x64False)(x62 x63False)x62 (x47 x64 x63)False)(∀ x63 x64 . (x62 x64False)(x62 x63False)x2 x63 (x1 x64)(x48 (x20 x63 x64) x64 x63False)False)(∀ x63 . (x60 x63False)x53 x63x59 x63(x54 (x29 x63) x63False)False)(∀ x63 . (x2 (x21 x63) x63False)False)((x38 x28False)False)((x59 x22False)False)((x62 x27False)False)(∀ x63 x64 x65 . (x62 x65False)(x62 x63False)x2 x63 (x1 x65)x48 x64 x65 x63(x2 x64 x65False)False)(∀ x63 x64 . (x60 x64False)x53 x64x59 x64x54 x63 x64(x48 x63 (x47 (x1 (x55 x64)) (x1 (x55 x64))) (x46 (x1 (x55 x64)) (x1 (x55 x64)) (x7 (x55 x64)) (x7 (x55 x64)))False)False)(∀ x63 . x59 x63(x38 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)(x2 (x56 x65 x63 x64) (x1 x65)False)False)(∀ x63 . (x2 (x7 x63) (x1 (x1 x63))False)False)(∀ x63 x64 x65 x66 . x2 x65 (x1 x66)x2 x64 (x1 x63)(x2 (x46 x66 x63 x65 x64) (x1 (x47 x66 x63))False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x2 (x51 x65 x64 x63) (x1 x65)False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x54 (x58 x65 x63 x64) x65False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x54 (x52 x65 x63 x64) x65False)False)(∀ x63 x64 . (x60 x64False)x53 x64x59 x64x54 x63 x64(x2 (x57 x64 x63) (x1 (x55 x64))False)False)(∀ x63 x64 . (x60 x64False)x53 x64x59 x64x54 x63 x64(x2 (x3 x64 x63) (x1 (x55 x64))False)False)(∀ x63 x64 . (x42 x64 x63 = x19 (x19 x64 x63) (x30 x64)False)False)((x61 = x27False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x58 x65 x63 x64 = x42 (x56 (x55 x65) (x3 x65 x63) (x3 x65 x64)) (x56 (x55 x65) (x57 x65 x63) (x57 x65 x64))False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65(x52 x65 x63 x64 = x42 (x51 (x55 x65) (x3 x65 x63) (x3 x65 x64)) (x51 (x55 x65) (x57 x65 x63) (x57 x65 x64))False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x3 x65 x63 = x3 x65 x64x57 x65 x63 = x57 x65 x64(x49 x65 x63 x64False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x49 x65 x63 x64(x57 x65 x63 = x57 x65 x64False)False)(∀ x63 x64 x65 . (x60 x65False)x53 x65x59 x65x54 x63 x65x54 x64 x65x49 x65 x63 x64(x3 x65 x63 = x3 x65 x64False)False)(∀ x63 x64 . (x60 x64False)x53 x64x59 x64x54 x63 x64(x57 x64 x63 = x44 x63False)False)(∀ x63 x64 . (x60 x64False)x53 x64x59 x64x54 x63 x64(x3 x64 x63 = x43 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)(x56 x65 x63 x64 = x56 x65 x64 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x51 x65 x64 x63 = x51 x65 x63 x64False)False)(∀ x63 x64 . (x50 x64 x63 = x50 x63 x64False)False)(∀ x63 x64 . (x5 x64 x63 = x5 x63 x64False)False)(∀ x63 x64 . (x19 x64 x63 = x19 x63 x64False)False)(∀ x63 . x38 x63x26 x63 x61(x60 x63False)False)(∀ x63 . x38 x63x60 x63(x26 x63 x61False)False)(∀ x63 . x38 x63(x17 x63False)x12 x63False)(∀ x63 . x38 x63x12 x63(x17 x63False)False)(∀ x63 x64 . x8 x64x2 x63 (x1 x64)(x8 x63False)False)(∀ x63 . x38 x63(x17 x63False)x17 x63False)(∀ x63 . x38 x63(x17 x63False)x60 x63False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)x40 x63 x64False)(∀ x63 . x38 x63x60 x63(x17 x63False)False)(∀ x63 . x38 x63x60 x63(x60 x63False)False)(∀ x63 x64 x65 . x62 x65x2 x63 (x1 (x47 x64 x65))(x62 x63False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)x62 x63(x40 x63 x64False)False)(∀ x63 x64 x65 . x62 x65x2 x63 (x1 (x47 x65 x64))(x62 x63False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)(x40 x63 x64False)x62 x63False)(∀ x63 . x38 x63(x12 x63False)x60 x63False)(∀ x63 x64 x65 . x2 x65 (x1 (x47 x63 x64))(x33 x65 x64False)False)(∀ x63 x64 x65 . x2 x65 (x1 (x47 x64 x63))(x16 x65 x64False)False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)(x62 x63False)False)(∀ x63 . x38 x63x60 x63(x12 x63False)False)(∀ x63 x64 x65 . x2 x65 (x1 (x47 x63 x64))(x31 x65False)False)(∀ x63 . x38 x63(x12 x63False)x60 x63False)(∀ x63 . x38 x63x26 x63 x6(x12 x63False)False)(∀ x63 . x38 x63x26 x63 x6x60 x63False)(∀ x63 . x38 x63(x60 x63False)x12 x63(x26 x63 x6False)False)(∀ x63 x64 . x0 x63 x64x0 x64 x63False)(x49 x23 (x52 x23 x25 (x58 x23 x25 x24)) x25False)((x54 x24 x23False)False)((x54 x25 x23False)False)((x59 x23False)False)((x53 x23False)False)(x60 x23False)False (proof)