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Proofgold Signed Transaction

vin
PrPhD../6a7ab..
PUgde../7edce..
vout
PrPhD../554d9.. 102.64 bars
TMHq7../3792b.. ownership of 3a9bd.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
TMdBD../c8e0a.. ownership of 37e8e.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
PUZwC../aef24.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 3a9bd.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 : ι → ι → ι . ∀ x5 x6 : ι → ο . ∀ x7 : ι → ι → ο . ∀ x8 : ι → ι → ι → ι . ∀ x9 : ι → ι → ι . ∀ x10 : ι → ι → ι → ι . ∀ x11 x12 : ι → ο . ∀ x13 : ι → ι . ∀ x14 x15 : ι → ι → ι → ι → ι . ∀ x16 : ι → ι . ∀ x17 : ι → ο . ∀ x18 x19 . ∀ x20 : ι → ι → ι → ι . ∀ x21 : ι → ι → ι → ι → ι . ∀ x22 x23 : ι → ο . ∀ x24 : ι → ι → ο . ∀ x25 x26 : ι → ι . ∀ x27 . ∀ x28 : ι → ι → ι . ∀ x29 : ι → ι → ι → ι . ∀ x30 x31 x32 : ι → ι . ∀ x33 x34 x35 x36 . ∀ x37 : ι → ι → ο . ∀ x38 : ι → ο . ∀ x39 : ι → ι → ι . ∀ x40 x41 : ι → ι → ι → ι . ∀ x42 x43 . ∀ x44 : ι → ι . ∀ x45 : ι → ι → ι → ι → ι . ∀ x46 : ι → ι → ι . ∀ x47 x48 : ι → ι . ∀ x49 x50 : ι → ο . ∀ x51 : ι → ι . ∀ x52 : ι → ι → ι . ∀ x53 . ∀ x54 : ι → ι → ι → ι . ∀ x55 x56 : ι → ι → ο . ∀ x57 . ∀ x58 : ι → ο . (∀ x59 x60 . x58 x60(x60 = x59False)x58 x59False)(∀ x59 x60 . x0 x59 x60x58 x60False)(∀ x59 . x58 x59(x59 = x57False)False)(∀ x59 x60 x61 . x0 x59 x60x2 x60 (x1 x61)x58 x61False)(∀ x59 x60 x61 . x0 x60 x61x2 x61 (x1 x59)(x2 x60 x59False)False)(∀ x59 x60 . x3 x60 x59(x2 x60 (x1 x59)False)False)(∀ x59 x60 . x2 x60 (x1 x59)(x3 x60 x59False)False)(∀ x59 x60 x61 . x0 x60 x61x0 x59 x61x0 x59 (x4 x61 x60)False)(∀ x59 x60 . x0 x60 x59(x0 (x4 x59 x60) x59False)False)(∀ x59 x60 . x2 x59 x60(x58 x60False)(x0 x59 x60False)False)(∀ x59 x60 . x0 x60 x59(x2 x60 x59False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60x10 x60 x59 (x9 x59 x60) = x8 x60 x59 (x9 x59 x60)(x7 x59 x60False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60x10 x60 x59 (x9 x59 x60) = x8 x60 x59 (x9 x59 x60)(x56 x59 x60False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60(x2 (x9 x59 x60) (x13 x60)False)(x7 x59 x60False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60(x2 (x9 x59 x60) (x13 x60)False)(x56 x59 x60False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x7 x60 x61x56 x60 x61x7 x60 x61x2 x59 (x13 x61)(x10 x61 x60 x59 = x8 x61 x60 x59False)False)(∀ x59 x60 x61 x62 x63 . (x5 x63False)x12 x63x6 x63x11 x63x2 x62 (x13 x63)x7 x59 x63x2 x61 (x13 x63)x60 = x54 x63 x61 x62x55 x59 x61(x0 x60 (x8 x63 x59 x62)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x8 x62 x59 x61)(x55 x59 (x14 x59 x61 x62 x60)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x8 x62 x59 x61)(x60 = x54 x62 (x14 x59 x61 x62 x60) x61False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x8 x62 x59 x61)(x2 (x14 x59 x61 x62 x60) (x13 x62)False)False)(∀ x59 x60 x61 x62 x63 . (x5 x63False)x12 x63x6 x63x11 x63x2 x62 (x13 x63)x7 x59 x63x2 x61 (x13 x63)x60 = x54 x63 x62 x61x55 x59 x61(x0 x60 (x10 x63 x59 x62)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x10 x62 x59 x61)(x55 x59 (x15 x59 x61 x62 x60)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x10 x62 x59 x61)(x60 = x54 x62 x61 (x15 x59 x61 x62 x60)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x12 x62x6 x62x11 x62x2 x61 (x13 x62)x7 x59 x62x0 x60 (x10 x62 x59 x61)(x2 (x15 x59 x61 x62 x60) (x13 x62)False)False)(x58 x53False)(∀ x59 . (x3 x59 x59False)False)(∀ x59 x60 . (x58 x60False)x2 x59 x60(x52 x60 x59 = x51 x59False)False)(∀ x59 . (x5 x59False)x17 x59x58 (x16 x59)False)(∀ x59 . (x5 x59False)x17 x59(x2 (x16 x59) (x1 (x13 x59))False)False)(x58 x18False)(∀ x59 . (x50 x59False)x17 x59x49 (x48 x59)False)(∀ x59 . (x50 x59False)x17 x59(x2 (x48 x59) (x1 (x13 x59))False)False)(∀ x59 . (x5 x59False)x17 x59(x49 (x47 x59)False)False)(∀ x59 . (x5 x59False)x17 x59x58 (x47 x59)False)(∀ x59 . (x5 x59False)x17 x59(x2 (x47 x59) (x1 (x13 x59))False)False)((x58 x19False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x2 x59 (x13 x60)(x46 x60 (x46 x60 x59) = x59False)False)(∀ x59 x60 x61 x62 x63 x64 . (x5 x64False)x11 x64x2 x63 (x1 (x13 x64))x2 x59 (x1 (x13 x64))x2 x62 (x13 x64)x2 x60 (x13 x64)x61 = x54 x64 x62 x60x0 x62 x63x0 x60 x59(x0 x61 (x20 x64 x63 x59)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x11 x62x2 x61 (x1 (x13 x62))x2 x59 (x1 (x13 x62))x0 x60 (x20 x62 x61 x59)(x0 (x45 x59 x61 x62 x60) x59False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x11 x62x2 x61 (x1 (x13 x62))x2 x59 (x1 (x13 x62))x0 x60 (x20 x62 x61 x59)(x0 (x21 x59 x61 x62 x60) x61False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x11 x62x2 x61 (x1 (x13 x62))x2 x59 (x1 (x13 x62))x0 x60 (x20 x62 x61 x59)(x60 = x54 x62 (x21 x59 x61 x62 x60) (x45 x59 x61 x62 x60)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x11 x62x2 x61 (x1 (x13 x62))x2 x59 (x1 (x13 x62))x0 x60 (x20 x62 x61 x59)(x2 (x45 x59 x61 x62 x60) (x13 x62)False)False)(∀ x59 x60 x61 x62 . (x5 x62False)x11 x62x2 x61 (x1 (x13 x62))x2 x59 (x1 (x13 x62))x0 x60 (x20 x62 x61 x59)(x2 (x21 x59 x61 x62 x60) (x13 x62)False)False)(∀ x59 . (x22 x59False)x17 x59x23 (x13 x59)False)(∀ x59 . x22 x59x17 x59(x23 (x13 x59)False)False)(∀ x59 . x50 x59x17 x59(x49 (x13 x59)False)False)(∀ x59 . (x50 x59False)x17 x59x49 (x13 x59)False)(∀ x59 . (x5 x59False)x12 x59x6 x59x11 x59x24 (x25 x59) x59False)(∀ x59 . x58 (x51 x59)False)(∀ x59 . (x5 x59False)x17 x59x58 (x13 x59)False)((x58 x57False)False)(∀ x59 . x5 x59x17 x59(x58 (x13 x59)False)False)(∀ x59 . (x2 (x44 x59) x59False)False)(∀ x59 . (x5 x59False)x12 x59x11 x59(x7 (x26 x59) x59False)False)((x11 x43False)False)((x17 x27False)False)((x58 x42False)False)(∀ x59 x60 . (x5 x60False)x12 x60x11 x60x7 x59 x60(x11 x59False)False)(∀ x59 x60 . (x5 x60False)x12 x60x11 x60x7 x59 x60(x12 x59False)False)(∀ x59 x60 . (x5 x60False)x12 x60x11 x60x7 x59 x60x5 x59False)(∀ x59 . x11 x59(x17 x59False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60(x2 (x28 x60 x59) (x1 (x13 x60))False)False)(∀ x59 x60 . (x58 x60False)x2 x59 x60(x2 (x52 x60 x59) (x1 x60)False)False)(∀ x59 x60 x61 . x11 x61x2 x59 (x13 x61)x2 x60 (x13 x61)(x2 (x54 x61 x59 x60) (x13 x61)False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x13 x61)x2 x59 (x1 (x13 x61))(x2 (x41 x61 x60 x59) (x1 (x13 x61))False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x13 x61)x2 x59 (x1 (x13 x61))(x2 (x29 x61 x60 x59) (x1 (x13 x61))False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x1 (x13 x61))x2 x59 (x1 (x13 x61))(x2 (x40 x61 x60 x59) (x1 (x13 x61))False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x2 x59 (x13 x60)(x2 (x46 x60 x59) (x13 x60)False)False)(∀ x59 . x11 x59(x2 (x25 x59) (x13 x59)False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x7 x60 x61x2 x59 (x13 x61)(x2 (x8 x61 x60 x59) (x1 (x13 x61))False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x7 x60 x61x2 x59 (x13 x61)(x2 (x10 x61 x60 x59) (x1 (x13 x61))False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60(x28 x60 x59 = x13 x59False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x2 x60 (x13 x61)x2 x59 (x13 x61)x54 x61 x60 x59 = x25 x61x54 x61 x59 x60 = x25 x61(x59 = x46 x61 x60False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x2 x60 (x13 x61)x2 x59 (x13 x61)x59 = x46 x61 x60(x54 x61 x59 x60 = x25 x61False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x2 x60 (x13 x61)x2 x59 (x13 x61)x59 = x46 x61 x60(x54 x61 x60 x59 = x25 x61False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x13 x61)x2 x59 (x1 (x13 x61))(x41 x61 x60 x59 = x40 x61 x59 (x52 (x13 x61) x60)False)False)(∀ x59 x60 . x11 x60x38 x60x2 x59 (x13 x60)x54 x60 (x39 x59 x60) x59 = x39 x59 x60x54 x60 x59 (x39 x59 x60) = x39 x59 x60(x59 = x25 x60False)False)(∀ x59 x60 . x11 x60x38 x60x2 x59 (x13 x60)(x2 (x39 x59 x60) (x13 x60)False)(x59 = x25 x60False)False)(∀ x59 x60 x61 . x11 x61x38 x61x2 x60 (x13 x61)x60 = x25 x61x2 x59 (x13 x61)(x54 x61 x60 x59 = x59False)False)(∀ x59 x60 x61 . x11 x61x38 x61x2 x60 (x13 x61)x60 = x25 x61x2 x59 (x13 x61)(x54 x61 x59 x60 = x59False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x13 x61)x2 x59 (x1 (x13 x61))(x29 x61 x60 x59 = x40 x61 (x52 (x13 x61) x60) x59False)False)(∀ x59 . x11 x59x54 x59 (x54 x59 (x32 x59) (x30 x59)) (x31 x59) = x54 x59 (x32 x59) (x54 x59 (x30 x59) (x31 x59))(x6 x59False)False)(∀ x59 . x11 x59(x2 (x31 x59) (x13 x59)False)(x6 x59False)False)(∀ x59 . x11 x59(x2 (x30 x59) (x13 x59)False)(x6 x59False)False)(∀ x59 . x11 x59(x2 (x32 x59) (x13 x59)False)(x6 x59False)False)(∀ x59 x60 x61 x62 . x11 x62x6 x62x2 x61 (x13 x62)x2 x59 (x13 x62)x2 x60 (x13 x62)(x54 x62 (x54 x62 x61 x59) x60 = x54 x62 x61 (x54 x62 x59 x60)False)False)((x57 = x42False)False)(∀ x59 x60 x61 . (x5 x61False)x11 x61x2 x60 (x1 (x13 x61))x2 x59 (x1 (x13 x61))(x40 x61 x60 x59 = x20 x61 x60 x59False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x7 x60 x61x2 x59 (x13 x61)(x8 x61 x60 x59 = x41 x61 x59 (x28 x61 x60)False)False)(∀ x59 x60 x61 . (x5 x61False)x12 x61x6 x61x11 x61x7 x60 x61x2 x59 (x13 x61)(x10 x61 x60 x59 = x29 x61 x59 (x28 x61 x60)False)False)(∀ x59 . x17 x59x37 x59 x57(x5 x59False)False)(∀ x59 . x17 x59x5 x59(x37 x59 x57False)False)(∀ x59 . x17 x59(x22 x59False)x50 x59False)(∀ x59 . x17 x59x50 x59(x22 x59False)False)(∀ x59 . x17 x59(x22 x59False)x22 x59False)(∀ x59 . x17 x59(x22 x59False)x5 x59False)(∀ x59 . x17 x59x5 x59(x22 x59False)False)(∀ x59 . x17 x59x5 x59(x5 x59False)False)(∀ x59 x60 . (x5 x60False)x22 x60x12 x60x6 x60x11 x60x7 x59 x60(x22 x59False)False)(∀ x59 . x17 x59(x50 x59False)x5 x59False)(∀ x59 . x17 x59x5 x59(x50 x59False)False)(∀ x59 x60 . (x5 x60False)x12 x60x6 x60x11 x60x7 x59 x60(x6 x59False)False)(∀ x59 . x11 x59x12 x59(x38 x59False)False)(∀ x59 . x17 x59(x50 x59False)x5 x59False)(∀ x59 . x17 x59x37 x59 x53(x50 x59False)False)(∀ x59 . x17 x59x37 x59 x53x5 x59False)(∀ x59 . x17 x59(x5 x59False)x50 x59(x37 x59 x53False)False)(∀ x59 x60 . x0 x59 x60x0 x60 x59False)(x55 x36 (x54 x33 (x54 x33 x35 x34) (x46 x33 x35))False)((x55 x36 x34False)False)((x7 x36 x33False)False)((x56 x36 x33False)False)((x2 x34 (x13 x33)False)False)((x2 x35 (x13 x33)False)False)((x11 x33False)False)((x6 x33False)False)((x12 x33False)False)(x5 x33False)False (proof)