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Proofgold Signed Transaction

vin
PrPhD../d0fc2..
PUhve../c78ef..
vout
PrPhD../12443.. 102.63 bars
TMP5V../a438c.. ownership of b434c.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
TMUzv../e4206.. ownership of 37912.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
PUdMN../ac5c8.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem b434c.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ο . ∀ x7 . ∀ x8 : ι → ο . ∀ x9 . ∀ x10 x11 x12 : ι → ι . ∀ x13 : ι → ι → ο . ∀ x14 x15 . ∀ x16 : ι → ο . ∀ x17 . ∀ x18 x19 : ι → ι . ∀ x20 x21 . ∀ x22 : ι → ο . ∀ x23 . ∀ x24 : ι → ι . ∀ x25 : ι → ι → ι . ∀ x26 : ι → ο . ∀ x27 x28 . ∀ x29 : ι → ο . ∀ x30 : ι → ι . ∀ x31 . ∀ x32 : ι → ο . ∀ x33 . ∀ x34 : ι → ο . ∀ x35 x36 x37 x38 . ∀ x39 x40 : ι → ο . ∀ x41 . ∀ x42 : ι → ο . ∀ x43 : ι → ι . ∀ x44 x45 . ∀ x46 : ι → ι . ∀ x47 . ∀ x48 : ι → ο . ∀ x49 . ∀ x50 : ι → ο . ∀ x51 : ι → ι . ∀ x52 : ι → ο . ∀ x53 . ∀ x54 x55 x56 : ι → ο . ∀ x57 : ι → ι → ο . ∀ x58 x59 : ι → ι . ∀ x60 : ι → ι → ι . ∀ x61 : ι → ο . ∀ x62 . ∀ x63 : ι → ο . (∀ x64 x65 . x63 x65(x65 = x64False)x63 x64False)(∀ x64 x65 . x0 x64 x65x63 x65False)(∀ x64 . x63 x64(x64 = x62False)False)(∀ x64 x65 x66 . x0 x64 x65x2 x65 (x1 x66)x63 x66False)(∀ x64 x65 x66 . x0 x65 x66x2 x66 (x1 x64)(x2 x65 x64False)False)(∀ x64 x65 . x3 x65 x64(x2 x65 (x1 x64)False)False)(∀ x64 x65 . x2 x65 (x1 x64)(x3 x65 x64False)False)(∀ x64 x65 . x2 x64 x65(x63 x65False)(x0 x64 x65False)False)(∀ x64 x65 . x61 x65x61 x64x3 (x58 x65) (x59 x64)(x59 (x60 x64 x65) = x59 x65False)False)(∀ x64 x65 . x61 x65x61 x64x3 (x59 x65) (x58 x64)(x58 (x60 x65 x64) = x58 x65False)False)(∀ x64 x65 . x0 x65 x64(x2 x65 x64False)False)((x2 x62 x4False)False)(∀ x64 x65 . x57 x64 x65(x57 x65 x64False)False)(∀ x64 . (x57 x64 x64False)False)(∀ x64 . (x3 x64 x64False)False)(∀ x64 x65 . x5 x65 x64(x57 x65 x64False)False)(∀ x64 x65 . x57 x65 x64(x5 x65 x64False)False)((x6 x7False)False)((x56 x7False)False)((x61 x7False)False)(x63 x7False)((x8 x9False)False)((x55 x9False)False)(x63 x9False)((x54 x53False)False)(x63 x53False)(∀ x64 . (x52 x64False)(x55 (x51 x64)False)False)(∀ x64 . (x52 x64False)x52 (x51 x64)False)(∀ x64 . (x52 x64False)(x2 (x51 x64) (x1 x64)False)False)(∀ x64 . (x52 x64False)x52 (x10 x64)False)(∀ x64 . (x52 x64False)(x2 (x10 x64) (x1 x64)False)False)(∀ x64 . (x63 x64False)(x52 (x11 x64)False)False)(∀ x64 . (x63 x64False)x63 (x11 x64)False)(∀ x64 . (x63 x64False)(x2 (x11 x64) (x1 x64)False)False)((x50 x49False)False)(x63 x49False)(x48 x47False)((x56 x47False)False)((x61 x47False)False)(∀ x64 . (x63 x64False)(x13 (x12 x64) x64False)False)(∀ x64 . (x63 x64False)(x2 (x12 x64) (x1 x64)False)False)((x50 x14False)False)(∀ x64 . x13 (x46 x64) x64False)(∀ x64 . (x2 (x46 x64) (x1 x64)False)False)((x55 x45False)False)((x56 x45False)False)((x61 x45False)False)(x63 x45False)(x52 x44False)(x63 x15False)(∀ x64 . (x63 (x43 x64)False)False)(∀ x64 . (x2 (x43 x64) (x1 x64)False)False)((x42 x41False)False)((x16 x41False)False)((x40 x41False)False)(x63 x41False)((x39 x38False)False)((x56 x38False)False)((x61 x38False)False)(x63 x17False)((x48 x17False)False)((x56 x17False)False)((x61 x17False)False)(∀ x64 . (x63 x64False)(x55 (x18 x64)False)False)(∀ x64 . (x63 x64False)x63 (x18 x64)False)(∀ x64 . (x63 x64False)(x2 (x18 x64) (x1 x64)False)False)((x52 x37False)False)(x63 x37False)((x63 x36False)False)(∀ x64 . (x63 x64False)x63 (x19 x64)False)(∀ x64 . (x63 x64False)(x2 (x19 x64) (x1 x64)False)False)((x42 x20False)False)((x56 x35False)False)((x61 x35False)False)((x34 x33False)False)((x56 x33False)False)((x61 x33False)False)((x55 x21False)False)(x63 x21False)((x22 x23False)False)(∀ x64 x65 . x61 x65x56 x65x34 x65x61 x64x56 x64(x34 (x60 x64 x65)False)False)(∀ x64 x65 . x61 x65x56 x65x34 x65x61 x64x56 x64(x61 (x60 x64 x65)False)False)(∀ x64 x65 . x61 x65x56 x65x39 x65x61 x64x56 x64x39 x64(x39 (x60 x65 x64)False)False)(∀ x64 x65 . x61 x65x56 x65x39 x65x61 x64x56 x64x39 x64(x61 (x60 x65 x64)False)False)((x42 x4False)False)(x63 x4False)(∀ x64 . x63 x64(x63 (x59 x64)False)False)(∀ x64 . x63 x64(x63 (x58 x64)False)False)(∀ x64 . x61 x64x56 x64x32 x64(x42 (x58 x64)False)False)(∀ x64 . x61 x64x6 x64(x8 (x59 x64)False)False)(∀ x64 . x55 x64(x8 (x1 x64)False)False)(∀ x64 x65 . x61 x65x56 x65x61 x64x56 x64(x56 (x60 x65 x64)False)False)(∀ x64 x65 . x61 x65x56 x65x61 x64x56 x64(x61 (x60 x65 x64)False)False)(∀ x64 . x61 x64x55 x64(x55 (x59 x64)False)False)(∀ x64 x65 . x61 x65x56 x65x61 x64x56 x64x55 x64(x55 (x60 x64 x65)False)False)(∀ x64 x65 . x61 x65x56 x65x61 x64x56 x64x55 x64(x61 (x60 x64 x65)False)False)((x63 x62False)False)(∀ x64 . x63 (x1 x64)False)(∀ x64 . x61 x64x55 x64(x55 (x58 x64)False)False)(∀ x64 . (x52 x64False)x61 x64x56 x64x52 (x58 x64)False)(∀ x64 . x55 x64(x55 (x1 x64)False)False)(∀ x64 . x61 x64x56 x64(x48 x64False)x52 (x59 x64)False)(∀ x64 . x61 x64x56 x64x48 x64(x52 (x59 x64)False)False)(∀ x64 . (x2 (x24 x64) x64False)False)((x63 x31False)False)(∀ x64 x65 . (x61 (x60 x64 x65)False)False)(∀ x64 x65 x66 . x61 x66x56 x66x39 x66x58 x66 = x64x59 x66 = x65(x57 x64 x65False)False)(∀ x64 x65 . x57 x65 x64(x59 (x25 x64 x65) = x64False)False)(∀ x64 x65 . x57 x64 x65(x58 (x25 x65 x64) = x64False)False)(∀ x64 x65 . x57 x65 x64(x39 (x25 x64 x65)False)False)(∀ x64 x65 . x57 x65 x64(x56 (x25 x64 x65)False)False)(∀ x64 x65 . x57 x65 x64(x61 (x25 x64 x65)False)False)((x62 = x31False)False)(∀ x64 x65 . x61 x65x56 x65x59 x65 = x64x0 (x58 x65) x4(x55 x64False)False)(∀ x64 . x55 x64(x0 (x58 (x30 x64)) x4False)False)(∀ x64 . x55 x64(x59 (x30 x64) = x64False)False)(∀ x64 . x55 x64(x56 (x30 x64)False)False)(∀ x64 . x55 x64(x61 (x30 x64)False)False)(∀ x64 . x63 x64(x29 x64False)False)(∀ x64 x65 . x54 x65x2 x64 (x1 x65)(x54 x64False)False)(∀ x64 . x63 x64x61 x64(x6 x64False)False)(∀ x64 . x63 x64x61 x64(x61 x64False)False)(∀ x64 . x2 x64 x4(x50 x64False)False)(∀ x64 x65 . x54 x65x2 x64 x65(x56 x64False)False)(∀ x64 x65 . x54 x65x2 x64 x65(x61 x64False)False)(∀ x64 x65 . x8 x65x2 x64 (x1 x65)(x8 x64False)False)(∀ x64 . x63 x64(x50 x64False)False)(∀ x64 . x63 x64(x54 x64False)False)(∀ x64 x65 . x8 x65x2 x64 x65(x55 x64False)False)(∀ x64 . x50 x64(x42 x64False)False)(∀ x64 . x52 x64x61 x64x56 x64(x48 x64False)False)(∀ x64 . x52 x64x61 x64x56 x64(x56 x64False)False)(∀ x64 . x52 x64x61 x64x56 x64(x61 x64False)False)(∀ x64 . x63 x64(x8 x64False)False)(∀ x64 x65 . x52 x65x2 x64 (x1 x65)(x52 x64False)False)(∀ x64 x65 . x42 x65x2 x64 x65(x42 x64False)False)(∀ x64 . x61 x64x56 x64(x48 x64False)(x56 x64False)False)(∀ x64 . x61 x64x56 x64(x48 x64False)(x61 x64False)False)(∀ x64 . x61 x64x56 x64(x48 x64False)x52 x64False)(∀ x64 . (x55 x64False)x52 x64False)(∀ x64 x65 . x63 x65x2 x64 (x1 x65)x13 x64 x65False)(∀ x64 . x63 x64(x32 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x48 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x56 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x61 x64False)False)(∀ x64 . x52 x64(x55 x64False)False)(∀ x64 x65 . (x63 x65False)x2 x64 (x1 x65)x63 x64(x13 x64 x65False)False)(∀ x64 . x63 x64(x42 x64False)False)(∀ x64 x65 . x61 x65x56 x65x2 x64 (x1 x65)(x56 x64False)False)(∀ x64 . x61 x64x56 x64x63 x64(x34 x64False)False)(∀ x64 . x61 x64x56 x64x63 x64(x56 x64False)False)(∀ x64 . x61 x64x56 x64x63 x64(x61 x64False)False)(∀ x64 . x50 x64(x22 x64False)False)(∀ x64 . (x52 x64False)x63 x64False)(∀ x64 x65 . (x63 x65False)x2 x64 (x1 x65)(x13 x64 x65False)x63 x64False)(∀ x64 . x40 x64x16 x64(x42 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x39 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x56 x64False)False)(∀ x64 . x63 x64x61 x64x56 x64(x61 x64False)False)(∀ x64 . x61 x64x56 x64x34 x64(x26 x64False)False)(∀ x64 . x61 x64x56 x64x34 x64(x56 x64False)False)(∀ x64 . x61 x64x56 x64x34 x64(x61 x64False)False)(∀ x64 x65 . x55 x65x2 x64 (x1 x65)(x55 x64False)False)(∀ x64 . x63 x64(x22 x64False)False)(∀ x64 . x63 x64(x52 x64False)False)(∀ x64 x65 . x63 x65x2 x64 (x1 x65)(x63 x64False)False)(∀ x64 . x42 x64(x16 x64False)False)(∀ x64 . x42 x64(x40 x64False)False)(∀ x64 . x63 x64(x56 x64False)False)(∀ x64 . x63 x64(x55 x64False)False)(∀ x64 . x22 x64(x42 x64False)False)(∀ x64 x65 . x29 x65x2 x64 (x1 x65)(x29 x64False)False)(∀ x64 x65 . x0 x64 x65x0 x65 x64False)(x55 x27False)((x55 x28False)False)((x57 x28 x27False)False)False (proof)