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Proofgold Signed Transaction

vin
PrNUD../e3c0d..
PUcxJ../760b8..
vout
PrNUD../26f0a.. 0.03 bars
TMLXw../61f86.. ownership of 44fca.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
TMYMS../52c04.. ownership of cc4d2.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
PUdVk../90e0d.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 44fca.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 : ι → ι . ∀ x5 : ι → ο . ∀ x6 x7 x8 : ι → ι → ι . ∀ x9 : ι → ι → ι → ι . ∀ x10 : ι → ι → ο . ∀ x11 : ι → ο . ∀ x12 . ∀ x13 : ι → ι → ο . ∀ x14 x15 x16 x17 : ι → ι . ∀ x18 : ι → ι → ο . ∀ x19 : ι → ι . ∀ x20 : ι → ο . ∀ x21 x22 : ι → ι . ∀ x23 . ∀ x24 : ι → ι . ∀ x25 : ι → ι → ο . ∀ x26 : ι → ο . ∀ x27 x28 : ι → ι . ∀ x29 : ι → ι → ο . ∀ x30 : ι → ι . ∀ x31 x32 . ∀ x33 : ι → ι . ∀ x34 x35 x36 x37 x38 . ∀ x39 x40 : ι → ο . ∀ x41 x42 . ∀ x43 : ι → ο . ∀ x44 : ι → ι → ο . ∀ x45 x46 x47 x48 : ι → ι . ∀ x49 : ι → ο . ∀ x50 : ι → ι . ∀ x51 x52 : ι → ο . ∀ x53 . ∀ x54 : ι → ο . ∀ x55 : ι → ι → ο . ∀ x56 x57 : ι → ι . ∀ x58 : 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 . x0 x64 x65x2 x65 (x1 x63)(x2 x64 x63False)False)(∀ x63 x64 . x3 x64 x63(x2 x64 (x1 x63)False)False)(∀ x63 x64 . x2 x64 (x1 x63)(x3 x64 x63False)False)(∀ x63 x64 . x2 x63 x64(x62 x64False)(x0 x63 x64False)False)(∀ x63 . x60 x63x54 x63x55 x63 (x58 (x57 x63) (x56 x63))(x59 x63False)False)(∀ x63 . x60 x63x54 x63(x2 (x56 x63) (x4 x63)False)(x59 x63False)False)(∀ x63 . x60 x63x54 x63(x2 (x57 x63) (x4 x63)False)(x59 x63False)False)(∀ x63 x64 x65 . x60 x65x54 x65x59 x65x2 x63 (x4 x65)x2 x64 (x4 x65)(x55 x65 (x58 x63 x64)False)False)(∀ x63 x64 . x0 x64 x63(x2 x64 x63False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))x0 (x6 x64 (x9 (x4 x64) (x7 x63 x64) (x8 x63 x64))) x63(x10 x63 x64False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))(x55 x64 (x9 (x4 x64) (x7 x63 x64) (x8 x63 x64))False)(x10 x63 x64False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))(x0 (x8 x63 x64) x63False)(x10 x63 x64False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))(x0 (x7 x63 x64) x63False)(x10 x63 x64False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))(x2 (x8 x63 x64) (x4 x64)False)(x10 x63 x64False)False)(∀ x63 x64 . (x5 x64False)x54 x64x2 x63 (x1 (x4 x64))(x2 (x7 x63 x64) (x4 x64)False)(x10 x63 x64False)False)(∀ x63 x64 x65 x66 . (x5 x66False)x54 x66x2 x65 (x1 (x4 x66))x10 x65 x66x2 x64 (x4 x66)x2 x63 (x4 x66)x0 x64 x65x0 x63 x65x55 x66 (x9 (x4 x66) x64 x63)(x0 (x6 x66 (x9 (x4 x66) x64 x63)) x65False)False)(x62 x53False)(∀ x63 . (x3 x63 x63False)False)(∀ x63 x64 x65 . (x62 x65False)x2 x63 x65x2 x64 x65(x9 x65 x63 x64 = x58 x63 x64False)False)((x11 x12False)False)((x52 x12False)False)(x62 x12False)(∀ x63 . (x51 x63False)(x52 (x50 x63)False)False)(∀ x63 . (x51 x63False)x51 (x50 x63)False)(∀ x63 . (x51 x63False)(x2 (x50 x63) (x1 x63)False)False)(∀ x63 . (x62 x63False)(x13 (x14 x63) x53False)False)(∀ x63 . (x62 x63False)(x2 (x14 x63) (x1 x63)False)False)(∀ x63 . (x51 x63False)x51 (x15 x63)False)(∀ x63 . (x51 x63False)(x2 (x15 x63) (x1 x63)False)False)(∀ x63 . (x62 x63False)(x51 (x16 x63)False)False)(∀ x63 . (x62 x63False)x62 (x16 x63)False)(∀ x63 . (x62 x63False)(x2 (x16 x63) (x1 x63)False)False)(∀ x63 . x49 x63(x13 (x48 x63) x63False)False)(∀ x63 . (x62 x63False)(x18 (x17 x63) x63False)False)(∀ x63 . (x62 x63False)(x2 (x17 x63) (x1 x63)False)False)(∀ x63 . (x5 x63False)x20 x63x62 (x19 x63)False)(∀ x63 . (x5 x63False)x20 x63(x2 (x19 x63) (x1 (x4 x63))False)False)(∀ x63 . (x52 x63False)x52 (x21 x63)False)(∀ x63 . (x52 x63False)(x2 (x21 x63) (x1 x63)False)False)(∀ x63 . x18 (x22 x63) x63False)(∀ x63 . (x2 (x22 x63) (x1 x63)False)False)(x52 x23False)(∀ x63 . (x62 (x47 x63)False)False)(∀ x63 . (x2 (x47 x63) (x1 x63)False)False)(∀ x63 . (x62 x63False)(x52 (x46 x63)False)False)(∀ x63 . (x62 x63False)x62 (x46 x63)False)(∀ x63 . (x62 x63False)(x2 (x46 x63) (x1 x63)False)False)(∀ x63 . x49 x63(x25 (x24 x63) x63False)False)(∀ x63 . x49 x63(x20 (x24 x63)False)False)(∀ x63 . (x26 x63False)x20 x63x51 (x27 x63)False)(∀ x63 . (x26 x63False)x20 x63(x2 (x27 x63) (x1 (x4 x63))False)False)(∀ x63 . (x5 x63False)x20 x63(x51 (x28 x63)False)False)(∀ x63 . (x5 x63False)x20 x63x62 (x28 x63)False)(∀ x63 . (x5 x63False)x20 x63(x2 (x28 x63) (x1 (x4 x63))False)False)(∀ x63 . x54 x63(x44 (x45 x63) x63False)False)(∀ x63 . x54 x63(x29 (x45 x63) x63False)False)(∀ x63 . x54 x63(x2 (x45 x63) (x1 (x4 x63))False)False)(∀ x63 . (x62 x63False)x62 (x30 x63)False)(∀ x63 . (x62 x63False)(x2 (x30 x63) (x1 x63)False)False)((x52 x31False)False)(x62 x31False)((x49 x32False)False)(∀ x63 . (x43 x63False)x20 x63x52 (x4 x63)False)(∀ x63 . (x52 x63False)x52 (x1 x63)False)(∀ x63 . x43 x63x20 x63(x52 (x4 x63)False)False)(∀ x63 . x26 x63x20 x63(x51 (x4 x63)False)False)(∀ x63 . (x26 x63False)x20 x63x51 (x4 x63)False)(∀ x63 x64 . x52 x64x52 x63(x11 (x58 x64 x63)False)False)(∀ x63 . x52 x63(x11 (x1 x63)False)False)(∀ x63 . (x5 x63False)x20 x63x62 (x4 x63)False)(∀ x63 x64 . (x52 (x58 x63 x64)False)False)(∀ x63 . x62 (x1 x63)False)(∀ x63 . x5 x63x20 x63(x62 (x4 x63)False)False)(∀ x63 x64 . x49 x64x25 x63 x64x20 x63(x13 (x4 x63) x64False)False)(∀ x63 . x52 x63(x52 (x1 x63)False)False)(∀ x63 . (x2 (x33 x63) x63False)False)((x20 x42False)False)((x54 x34False)False)((x62 x41False)False)(∀ x63 . x54 x63(x20 x63False)False)(∀ x63 x64 x65 . (x62 x65False)x2 x63 x65x2 x64 x65(x2 (x9 x65 x63 x64) (x1 x65)False)False)(∀ x63 x64 . x54 x64(x2 (x6 x64 x63) (x4 x64)False)False)((x61 = x41False)False)(∀ x63 x64 x65 . (x62 x65False)x2 x63 x65x2 x64 x65(x9 x65 x63 x64 = x9 x65 x64 x63False)False)(∀ x63 x64 . (x58 x64 x63 = x58 x63 x64False)False)(∀ x63 . x20 x63x25 x63 x61(x5 x63False)False)(∀ x63 . x13 x63 x53(x51 x63False)False)(∀ x63 . x13 x63 x53x62 x63False)(∀ x63 . x20 x63x5 x63(x25 x63 x61False)False)(∀ x63 x64 . x11 x64x2 x63 (x1 x64)(x11 x63False)False)(∀ x63 . x62 x63(x13 x63 x61False)False)(∀ x63 . x20 x63(x43 x63False)x26 x63False)(∀ x63 x64 . x11 x64x2 x63 x64(x52 x63False)False)(∀ x63 . x13 x63 x61(x62 x63False)False)(∀ x63 . x20 x63x26 x63(x43 x63False)False)(∀ x63 . x62 x63(x11 x63False)False)(∀ x63 . x40 x63x52 x63(x39 x63False)False)(∀ x63 x64 . x51 x64x2 x63 (x1 x64)(x51 x63False)False)(∀ x63 . x20 x63(x43 x63False)x43 x63False)(∀ x63 . x20 x63(x43 x63False)x5 x63False)(∀ x63 . (x52 x63False)x51 x63False)(∀ x63 . x39 x63(x52 x63False)False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)x18 x63 x64False)(∀ x63 . x20 x63x5 x63(x43 x63False)False)(∀ x63 . x20 x63x5 x63(x5 x63False)False)(∀ x63 . x51 x63(x52 x63False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)x62 x63(x18 x63 x64False)False)(∀ x63 . x39 x63(x49 x63False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)(x18 x63 x64False)x62 x63False)(∀ x63 . x20 x63(x26 x63False)x5 x63False)(∀ x63 x64 . x52 x64x2 x63 (x1 x64)(x52 x63False)False)(∀ x63 . x62 x63(x49 x63False)False)(∀ x63 x64 . x54 x64x2 x63 (x1 (x4 x64))x62 x63(x44 x63 x64False)False)(∀ x63 x64 . x54 x64x2 x63 (x1 (x4 x64))x62 x63(x29 x63 x64False)False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)(x62 x63False)False)(∀ x63 . x20 x63x5 x63(x26 x63False)False)(∀ x63 . x54 x63x59 x63x5 x63False)(∀ x63 . x62 x63(x52 x63False)False)(∀ x63 . x49 x63(x40 x63False)False)(∀ x63 . x20 x63(x26 x63False)x5 x63False)(∀ x63 . x20 x63x25 x63 x53(x26 x63False)False)(∀ x63 . x20 x63x25 x63 x53x5 x63False)(∀ x63 . x20 x63(x5 x63False)x26 x63(x25 x63 x53False)False)(∀ x63 . (x62 x63False)x51 x63(x13 x63 x53False)False)(∀ x63 x64 . x0 x63 x64x0 x64 x63False)(∀ x63 x64 . x2 x64 (x4 x35)x2 x63 (x4 x35)x0 x64 x36x0 x63 x36(x0 (x6 x35 (x9 (x4 x35) x64 x63)) x36False)(x10 x36 x35False)False)(x10 x36 x35x0 (x6 x35 (x9 (x4 x35) x37 x38)) x36False)(x10 x36 x35(x0 x38 x36False)False)(x10 x36 x35(x0 x37 x36False)False)(x10 x36 x35(x2 x38 (x4 x35)False)False)(x10 x36 x35(x2 x37 (x4 x35)False)False)((x2 x36 (x1 (x4 x35))False)False)((x54 x35False)False)((x59 x35False)False)((x60 x35False)False)False (proof)