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Proofgold Signed Transaction

vin
PrPhD../95d63..
PUf5Y../60df1..
vout
PrPhD../744d7.. 102.64 bars
TMWm9../d7996.. ownership of ed1ff.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
TMREv../23254.. ownership of 6a902.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
PUMYL../fca70.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem ed1ff.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 : ι → ι . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι → ο . ∀ x7 . ∀ x8 : ι → ι → ο . ∀ x9 : ι → ο . ∀ x10 : ι → ι → ο . ∀ x11 : ι → ι . ∀ x12 : ι → ο . ∀ x13 . ∀ x14 : ι → ι → ο . ∀ x15 : ι → ι . ∀ x16 x17 . ∀ x18 : ι → ο . ∀ x19 x20 . ∀ x21 : ι → ι → ο . ∀ x22 : ι → ι → ι . ∀ x23 x24 x25 : ι → ο . ∀ x26 : ι → ι . ∀ x27 . ∀ x28 : ι → ι → ο . ∀ x29 : ι → ο . ∀ x30 x31 x32 x33 x34 x35 x36 . ∀ x37 x38 : ι → ι → ι → ι → ι → ι . ∀ x39 : ι → ι → ι → ι → ι . ∀ x40 : ι → ι → ι → ι → ο . ∀ x41 x42 . ∀ x43 : ι → ι . ∀ x44 . ∀ x45 : ι → ο . ∀ x46 . ∀ x47 : ι → ι → ι . ∀ x48 . ∀ x49 : ι → ι → ο . ∀ x50 x51 x52 : ι → ι . ∀ x53 x54 : ι → ο . ∀ x55 x56 . ∀ x57 x58 : ι → ι → ι . ∀ x59 . ∀ x60 : ι → ο . ∀ x61 : ι → ι → ι . ∀ x62 . ∀ x63 x64 : ι → ο . ∀ x65 : ι → ι . ∀ x66 : ι → ι → ι → ι → ι → ι → ο . ∀ x67 : ι → ι → ο . ∀ x68 : ι → ο . ∀ x69 : ι → ι → ι → ο . ∀ x70 x71 : ι → ι → ι . ∀ x72 : ι → ο . ∀ x73 . ∀ x74 : ι → ο . (∀ x75 x76 . x74 x76(x76 = x75False)x74 x75False)(∀ x75 x76 . x0 x75 x76x74 x76False)(∀ x75 . x74 x75(x75 = x73False)False)(∀ x75 x76 x77 . x0 x75 x76x2 x76 (x1 x77)x74 x77False)(∀ x75 x76 x77 x78 . x72 x78x69 x78 x75 x76x2 x78 (x1 (x70 x75 x76))x0 x77 x75(x76 = x73False)(x0 (x71 x78 x77) x76False)False)(∀ x75 x76 x77 x78 x79 x80 . x3 x80x6 x75 x80x2 x79 (x4 x80)x2 x76 (x4 x80)x2 x78 (x4 x75)x2 x77 (x4 x75)x78 = x79x77 = x76x5 x75 x78 x77(x5 x80 x79 x76False)False)(∀ x75 x76 x77 . (x68 x77False)x3 x77(x68 x76False)x6 x76 x77x2 x75 (x4 x76)(x2 x75 (x4 x77)False)False)(∀ x75 x76 x77 . x0 x76 x77x2 x77 (x1 x75)(x2 x76 x75False)False)(∀ x75 x76 . x67 x76 x75(x2 x76 (x1 x75)False)False)(∀ x75 x76 . x2 x76 (x1 x75)(x67 x76 x75False)False)(∀ x75 x76 . x2 x75 x76(x74 x76False)(x0 x75 x76False)False)(∀ x75 x76 . x0 x76 x75(x2 x76 x75False)False)(∀ x75 x76 x77 x78 x79 x80 . (x74 x80False)(x74 x75False)x72 x79x69 x79 x76 x80x2 x79 (x1 (x70 x76 x80))x72 x77x69 x77 x78 x75x2 x77 (x1 (x70 x78 x75))x66 x76 x80 x78 x75 x79 x77(x66 x76 x80 x78 x75 x77 x79False)False)(x74 x7False)(∀ x75 . (x67 x75 x75False)False)(∀ x75 x76 x77 x78 x79 x80 . (x74 x80False)(x74 x75False)x72 x79x69 x79 x76 x80x2 x79 (x1 (x70 x76 x80))x72 x77x69 x77 x78 x75x2 x77 (x1 (x70 x78 x75))(x66 x76 x80 x78 x75 x79 x79False)False)(∀ x75 x76 x77 x78 x79 x80 . (x74 x80False)(x74 x75False)x72 x79x69 x79 x76 x80x2 x79 (x1 (x70 x76 x80))x72 x77x69 x77 x78 x75x2 x77 (x1 (x70 x78 x75))x79 = x77(x66 x76 x80 x78 x75 x79 x77False)False)(∀ x75 x76 x77 x78 x79 x80 . (x74 x80False)(x74 x75False)x72 x79x69 x79 x76 x80x2 x79 (x1 (x70 x76 x80))x72 x77x69 x77 x78 x75x2 x77 (x1 (x70 x78 x75))x66 x76 x80 x78 x75 x79 x77(x79 = x77False)False)(∀ x75 . (x72 (x65 x75)False)False)(∀ x75 . (x8 (x65 x75) x75False)False)(∀ x75 . (x64 (x65 x75)False)False)(∀ x75 . (x9 (x65 x75)False)False)((x63 x62False)False)(x74 x62False)(∀ x75 x76 . (x72 (x61 x75 x76)False)False)(∀ x75 x76 . (x10 (x61 x75 x76) x75False)False)(∀ x75 x76 . (x8 (x61 x76 x75) x75False)False)(∀ x75 x76 . (x9 (x61 x75 x76)False)False)(x60 x59False)((x72 x59False)False)((x9 x59False)False)(∀ x75 . (x68 x75False)x12 x75x74 (x11 x75)False)(∀ x75 . (x68 x75False)x12 x75(x2 (x11 x75) (x1 (x4 x75))False)False)((x72 x13False)False)((x64 x13False)False)((x9 x13False)False)(x74 x13False)(∀ x75 . (x14 (x15 x75) x75False)False)(∀ x75 . (x72 (x15 x75)False)False)(∀ x75 . (x8 (x15 x75) x75False)False)(∀ x75 . (x64 (x15 x75)False)False)(∀ x75 . (x9 (x15 x75)False)False)(∀ x75 x76 . (x10 (x58 x75 x76) x75False)False)(∀ x75 x76 . (x8 (x58 x76 x75) x75False)False)(∀ x75 x76 . (x9 (x58 x75 x76)False)False)((x72 x16False)False)((x64 x16False)False)((x9 x16False)False)(∀ x75 x76 . (x74 x76False)(x14 (x57 x76 x75) x75False)False)(∀ x75 x76 . (x74 x76False)(x72 (x57 x76 x75)False)False)(∀ x75 x76 . (x74 x76False)(x10 (x57 x76 x75) x76False)False)(∀ x75 x76 . (x74 x76False)(x8 (x57 x76 x75) x75False)False)(∀ x75 x76 . (x74 x76False)(x9 (x57 x76 x75)False)False)(∀ x75 x76 . (x74 x76False)(x2 (x57 x76 x75) (x1 (x70 x75 x76))False)False)(x74 x56False)((x64 x17False)False)((x9 x17False)False)((x18 x19False)False)((x72 x19False)False)((x9 x19False)False)(x74 x55False)((x60 x55False)False)((x72 x55False)False)((x9 x55False)False)(∀ x75 . (x54 x75False)x12 x75x53 (x52 x75)False)(∀ x75 . (x54 x75False)x12 x75(x2 (x52 x75) (x1 (x4 x75))False)False)(∀ x75 . (x68 x75False)x12 x75(x53 (x51 x75)False)False)(∀ x75 . (x68 x75False)x12 x75x74 (x51 x75)False)(∀ x75 . (x68 x75False)x12 x75(x2 (x51 x75) (x1 (x4 x75))False)False)((x74 x20False)False)(∀ x75 . x3 x75(x49 (x50 x75) x75False)False)(∀ x75 . x3 x75(x21 (x50 x75) x75False)False)(∀ x75 . x3 x75(x2 (x50 x75) (x1 (x4 x75))False)False)(∀ x75 x76 . (x10 (x22 x75 x76) x75False)False)(∀ x75 x76 . (x8 (x22 x76 x75) x75False)False)(∀ x75 x76 . (x9 (x22 x75 x76)False)False)(∀ x75 x76 . (x74 (x22 x75 x76)False)False)(∀ x75 x76 . (x2 (x22 x75 x76) (x1 (x70 x76 x75))False)False)((x9 x48False)False)(x74 x48False)(∀ x75 x76 . (x69 (x47 x75 x76) x76 x75False)False)(∀ x75 x76 . (x72 (x47 x75 x76)False)False)(∀ x75 x76 . (x10 (x47 x75 x76) x75False)False)(∀ x75 x76 . (x8 (x47 x76 x75) x75False)False)(∀ x75 x76 . (x9 (x47 x75 x76)False)False)(∀ x75 x76 . (x2 (x47 x75 x76) (x1 (x70 x76 x75))False)False)((x72 x46False)False)((x9 x46False)False)((x45 x44False)False)((x72 x44False)False)((x9 x44False)False)(∀ x75 . (x23 x75False)x12 x75x24 (x4 x75)False)(∀ x75 . x23 x75x12 x75(x24 (x4 x75)False)False)(∀ x75 x76 . x9 x76x72 x76x45 x76(x72 (x71 x76 x75)False)False)(∀ x75 x76 . x9 x76x72 x76x45 x76(x9 (x71 x76 x75)False)False)(∀ x75 . x54 x75x12 x75(x53 (x4 x75)False)False)(∀ x75 . (x54 x75False)x12 x75x53 (x4 x75)False)(∀ x75 x76 . (x9 (x70 x75 x76)False)False)(∀ x75 . (x68 x75False)x12 x75x74 (x4 x75)False)((x74 x73False)False)(∀ x75 . x68 x75x12 x75(x74 (x4 x75)False)False)(∀ x75 x76 . x9 x76x25 x76x72 x76(x74 (x71 x76 x75)False)False)(∀ x75 x76 x77 . x63 x77x9 x75x10 x75 x77x72 x75(x72 (x71 x75 x76)False)False)(∀ x75 x76 x77 . x63 x77x9 x75x10 x75 x77x72 x75(x9 (x71 x75 x76)False)False)(∀ x75 . x3 x75(x6 (x43 x75) x75False)False)(∀ x75 . (x2 (x26 x75) x75False)False)((x12 x42False)False)((x3 x27False)False)((x74 x41False)False)(∀ x75 x76 . x3 x76x6 x75 x76(x3 x75False)False)(∀ x75 . x3 x75(x12 x75False)False)((x73 = x41False)False)(∀ x75 x76 x77 x78 x79 x80 . x3 x80x72 x75x69 x75 x79 (x4 x80)x2 x75 (x1 (x70 x79 (x4 x80)))x72 x78x69 x78 x79 (x4 x80)x2 x78 (x1 (x70 x79 (x4 x80)))x2 x76 (x4 x80)x2 x77 (x4 x80)x76 = x71 x75 (x39 x78 x75 x80 x79)x77 = x71 x78 (x39 x78 x75 x80 x79)x5 x80 x76 x77(x40 x79 x80 x75 x78False)False)(∀ x75 x76 x77 x78 . x3 x78x72 x75x69 x75 x77 (x4 x78)x2 x75 (x1 (x70 x77 (x4 x78)))x72 x76x69 x76 x77 (x4 x78)x2 x76 (x1 (x70 x77 (x4 x78)))(x0 (x39 x76 x75 x78 x77) x77False)(x40 x77 x78 x75 x76False)False)(∀ x75 x76 x77 x78 x79 . x3 x79x72 x75x69 x75 x78 (x4 x79)x2 x75 (x1 (x70 x78 (x4 x79)))x72 x77x69 x77 x78 (x4 x79)x2 x77 (x1 (x70 x78 (x4 x79)))x40 x78 x79 x75 x77x0 x76 x78(x5 x79 (x37 x76 x77 x75 x79 x78) (x38 x76 x77 x75 x79 x78)False)False)(∀ x75 x76 x77 x78 x79 . x3 x79x72 x75x69 x75 x78 (x4 x79)x2 x75 (x1 (x70 x78 (x4 x79)))x72 x77x69 x77 x78 (x4 x79)x2 x77 (x1 (x70 x78 (x4 x79)))x40 x78 x79 x75 x77x0 x76 x78(x38 x76 x77 x75 x79 x78 = x71 x77 x76False)False)(∀ x75 x76 x77 x78 x79 . x3 x79x72 x75x69 x75 x78 (x4 x79)x2 x75 (x1 (x70 x78 (x4 x79)))x72 x77x69 x77 x78 (x4 x79)x2 x77 (x1 (x70 x78 (x4 x79)))x40 x78 x79 x75 x77x0 x76 x78(x37 x76 x77 x75 x79 x78 = x71 x75 x76False)False)(∀ x75 x76 x77 x78 x79 . x3 x79x72 x75x69 x75 x78 (x4 x79)x2 x75 (x1 (x70 x78 (x4 x79)))x72 x77x69 x77 x78 (x4 x79)x2 x77 (x1 (x70 x78 (x4 x79)))x40 x78 x79 x75 x77x0 x76 x78(x2 (x38 x76 x77 x75 x79 x78) (x4 x79)False)False)(∀ x75 x76 x77 x78 x79 . x3 x79x72 x75x69 x75 x78 (x4 x79)x2 x75 (x1 (x70 x78 (x4 x79)))x72 x77x69 x77 x78 (x4 x79)x2 x77 (x1 (x70 x78 (x4 x79)))x40 x78 x79 x75 x77x0 x76 x78(x2 (x37 x76 x77 x75 x79 x78) (x4 x79)False)False)(∀ x75 . x12 x75x28 x75 x73(x68 x75False)False)(∀ x75 x76 . x63 x76x2 x75 (x1 x76)(x63 x75False)False)(∀ x75 . x12 x75x68 x75(x28 x75 x73False)False)(∀ x75 x76 . x74 x76x9 x75x10 x75 x76(x10 x75 x76False)False)(∀ x75 x76 . x74 x76x9 x75x10 x75 x76(x9 x75False)False)(∀ x75 x76 . x74 x76x9 x75x10 x75 x76(x74 x75False)False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x76 (x1 (x70 x77 x75))x72 x76x69 x76 x77 x75(x69 x76 x77 x75False)False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x76 (x1 (x70 x77 x75))x72 x76x69 x76 x77 x75x74 x76False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x76 (x1 (x70 x77 x75))x72 x76x69 x76 x77 x75(x72 x76False)False)(∀ x75 x76 . x63 x76x2 x75 x76(x72 x75False)False)(∀ x75 x76 . x63 x76x2 x75 x76(x9 x75False)False)(∀ x75 . x12 x75(x23 x75False)x54 x75False)(∀ x75 x76 . x74 x76x9 x75x8 x75 x76(x8 x75 x76False)False)(∀ x75 x76 . x74 x76x9 x75x8 x75 x76(x9 x75False)False)(∀ x75 x76 . x74 x76x9 x75x8 x75 x76(x74 x75False)False)(∀ x75 . x74 x75(x63 x75False)False)(∀ x75 . x12 x75x54 x75(x23 x75False)False)(∀ x75 x76 x77 . x9 x77x10 x77 x75x2 x76 (x1 x77)(x10 x76 x75False)False)(∀ x75 . x53 x75x9 x75x72 x75(x60 x75False)False)(∀ x75 . x53 x75x9 x75x72 x75(x72 x75False)False)(∀ x75 . x53 x75x9 x75x72 x75(x9 x75False)False)(∀ x75 . x12 x75(x23 x75False)x23 x75False)(∀ x75 . x12 x75(x23 x75False)x68 x75False)(∀ x75 x76 x77 . x9 x77x8 x77 x75x2 x76 (x1 x77)(x8 x76 x75False)False)(∀ x75 . x9 x75x72 x75(x60 x75False)(x72 x75False)False)(∀ x75 . x9 x75x72 x75(x60 x75False)(x9 x75False)False)(∀ x75 . x9 x75x72 x75(x60 x75False)x53 x75False)(∀ x75 . x12 x75x68 x75(x23 x75False)False)(∀ x75 . x12 x75x68 x75(x68 x75False)False)(∀ x75 x76 x77 . x74 x77x2 x75 (x1 (x70 x76 x77))(x74 x75False)False)(∀ x75 . x74 x75x9 x75(x64 x75False)False)(∀ x75 . x74 x75x9 x75(x9 x75False)False)(∀ x75 x76 . x2 x76 (x1 (x70 x75 x75))x69 x76 x75 x75(x14 x76 x75False)False)(∀ x75 . x74 x75x9 x75x72 x75(x60 x75False)False)(∀ x75 . x74 x75x9 x75x72 x75(x72 x75False)False)(∀ x75 . x74 x75x9 x75x72 x75(x9 x75False)False)(∀ x75 x76 x77 . x74 x77x2 x75 (x1 (x70 x77 x76))(x74 x75False)False)(∀ x75 . x74 x75x9 x75(x25 x75False)False)(∀ x75 . x74 x75x9 x75(x9 x75False)False)(∀ x75 x76 x77 . (x74 x77False)x2 x75 (x1 (x70 x76 x77))x69 x75 x76 x77(x14 x75 x76False)False)(∀ x75 x76 . x9 x76x72 x76x2 x75 (x1 x76)(x72 x75False)False)(∀ x75 . x9 x75x72 x75x74 x75(x45 x75False)False)(∀ x75 . x9 x75x72 x75x74 x75(x72 x75False)False)(∀ x75 . x9 x75x72 x75x74 x75(x9 x75False)False)(∀ x75 . x12 x75(x54 x75False)x68 x75False)(∀ x75 x76 x77 . x2 x77 (x1 (x70 x75 x76))(x10 x77 x76False)False)(∀ x75 x76 x77 . x2 x77 (x1 (x70 x76 x75))(x8 x77 x76False)False)(∀ x75 x76 . x9 x76x2 x75 (x1 x76)(x9 x75False)False)(∀ x75 x76 x77 . x74 x77x2 x75 (x1 (x70 x77 x76))x69 x75 x77 x76(x14 x75 x77False)False)(∀ x75 . x74 x75x9 x75x72 x75(x18 x75False)False)(∀ x75 . x74 x75x9 x75x72 x75(x72 x75False)False)(∀ x75 . x74 x75x9 x75x72 x75(x9 x75False)False)(∀ x75 . x9 x75x72 x75x45 x75(x29 x75False)False)(∀ x75 . x9 x75x72 x75x45 x75(x72 x75False)False)(∀ x75 . x9 x75x72 x75x45 x75(x9 x75False)False)(∀ x75 x76 . x3 x76x2 x75 (x1 (x4 x76))x74 x75(x49 x75 x76False)False)(∀ x75 x76 . x3 x76x2 x75 (x1 (x4 x76))x74 x75(x21 x75 x76False)False)(∀ x75 . x12 x75x68 x75(x54 x75False)False)(∀ x75 x76 x77 . x2 x77 (x1 (x70 x75 x76))(x9 x77False)False)(∀ x75 . x74 x75(x9 x75False)False)(∀ x75 x76 x77 . x2 x76 (x1 (x70 x77 x75))x14 x76 x77(x69 x76 x77 x75False)False)(∀ x75 . x74 x75(x72 x75False)False)(∀ x75 x76 . x63 x76x9 x75x10 x75 x76x72 x75(x45 x75False)False)(∀ x75 x76 . x63 x76x9 x75x10 x75 x76x72 x75(x72 x75False)False)(∀ x75 x76 . x63 x76x9 x75x10 x75 x76x72 x75(x9 x75False)False)(∀ x75 . x12 x75(x54 x75False)x68 x75False)(∀ x75 . x12 x75x28 x75 x7(x54 x75False)False)(∀ x75 . x12 x75x28 x75 x7x68 x75False)(∀ x75 . x12 x75(x68 x75False)x54 x75(x28 x75 x7False)False)(∀ x75 x76 . x0 x75 x76x0 x76 x75False)(x40 x30 x33 x32 x31False)((x40 x30 x34 x35 x36False)False)((x66 x30 (x4 x33) x30 (x4 x34) x31 x36False)False)((x66 x30 (x4 x33) x30 (x4 x34) x32 x35False)False)((x2 x31 (x1 (x70 x30 (x4 x33)))False)False)((x69 x31 x30 (x4 x33)False)False)((x72 x31False)False)((x2 x32 (x1 (x70 x30 (x4 x33)))False)False)((x69 x32 x30 (x4 x33)False)False)((x72 x32False)False)((x2 x36 (x1 (x70 x30 (x4 x34)))False)False)((x69 x36 x30 (x4 x34)False)False)((x72 x36False)False)((x2 x35 (x1 (x70 x30 (x4 x34)))False)False)((x69 x35 x30 (x4 x34)False)False)((x72 x35False)False)((x6 x34 x33False)False)(x68 x34False)((x3 x33False)False)(x68 x33False)False (proof)