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Proofgold Signed Transaction

vin
PrPhD../00976..
PUYk9../16286..
vout
PrPhD../e0e2b.. 3.40 bars
TMZ3u../bbfdb.. ownership of d176f.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
TMJEC../3a9a0.. ownership of 6b566.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
PUMyU../4d71b.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem d176f.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 : ι → ο . ∀ x7 . ∀ x8 : ι → ο . ∀ x9 : ι → ι → ο . ∀ x10 : ι → ι . ∀ x11 : ι → ι → ο . ∀ x12 x13 : ι → ι . ∀ x14 : ι → ι → ο . ∀ x15 : ι → ο . ∀ x16 . ∀ x17 : ι → ο . ∀ x18 : ι → ι . ∀ x19 : ι → ι → ο . ∀ x20 : ι → ι . ∀ x21 : ι → ο . ∀ x22 . ∀ x23 : ι → ι . ∀ x24 : ι → ο . ∀ x25 . ∀ x26 x27 x28 x29 : ι → ο . ∀ x30 . ∀ x31 x32 x33 : ι → ο . ∀ x34 x35 . ∀ x36 x37 x38 : ι → ο . ∀ x39 . ∀ x40 : ι → ι . ∀ x41 x42 : ι → ο . ∀ x43 : ι → ι . ∀ x44 x45 . ∀ x46 x47 : ι → ι . ∀ x48 x49 x50 . ∀ x51 : ι → ο . ∀ x52 : ι → ι . ∀ x53 : ι → ι → ο . ∀ x54 . ∀ x55 x56 : ι → ο . ∀ x57 : ι → ι . ∀ x58 : ι → ι → ι → ι . ∀ x59 : ι → ι → ι . ∀ 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 x64 x65 . x60 x65x2 x63 (x1 (x57 x65))x2 x64 (x1 (x57 x65))(x3 (x58 (x57 x65) (x59 x65 x63) (x59 x65 x64)) (x59 x65 (x58 (x57 x65) x63 x64))False)False)(∀ x63 x64 x65 . x3 x64 x65x3 x65 x63(x3 x64 x63False)False)(∀ x63 x64 . x0 x64 x63(x2 x64 x63False)False)(∀ x63 . (x4 x63 x61 = x63False)False)(∀ x63 x64 x65 . x60 x65x2 x63 (x1 (x57 x65))x2 x64 (x1 (x57 x65))x3 x63 x64(x3 (x59 x65 x63) (x59 x65 x64)False)False)(∀ x63 x64 x65 . x60 x65x2 x63 (x1 (x57 x65))x2 x64 (x1 (x57 x65))x3 x63 x64(x3 (x5 x65 x63) (x5 x65 x64)False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))(x3 x63 (x5 x64 x63)False)False)(∀ x63 x64 x65 x66 . x3 x65 x66x3 x64 x63(x3 (x4 x65 x64) (x4 x66 x63)False)False)(∀ x63 x64 . x3 x64 x63(x4 x64 x63 = x63False)False)(∀ x63 . (x3 x63 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x58 x65 x64 x63 = x4 x64 x63False)False)((x6 x7False)False)(x62 x7False)(∀ x63 . x8 x63x60 x63(x9 (x10 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x2 (x10 x63) (x1 (x57 x63))False)False)(∀ x63 . x8 x63x60 x63(x11 (x12 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x2 (x12 x63) (x1 (x57 x63))False)False)(∀ x63 . x60 x63(x14 (x13 x63) x63False)False)(∀ x63 . x60 x63(x2 (x13 x63) (x1 (x57 x63))False)False)((x15 x16False)False)((x56 x16False)False)((x17 x16False)False)((x62 x16False)False)(∀ x63 . (x62 x63False)(x19 (x18 x63) x63False)False)(∀ x63 . (x62 x63False)(x2 (x18 x63) (x1 x63)False)False)(∀ x63 . x19 (x20 x63) x63False)(∀ x63 . (x2 (x20 x63) (x1 x63)False)False)((x21 x22False)False)((x55 x22False)False)(x62 x22False)(x62 x54False)(∀ x63 . x8 x63x60 x63(x11 (x23 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x53 (x23 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x2 (x23 x63) (x1 (x57 x63))False)False)(∀ x63 . (x62 (x52 x63)False)False)(∀ x63 . (x2 (x52 x63) (x1 x63)False)False)((x51 x50False)False)((x24 x50False)False)((x55 x49False)False)(x62 x49False)((x15 x48False)False)((x62 x25False)False)(∀ x63 . x8 x63x60 x63(x53 (x47 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x2 (x47 x63) (x1 (x57 x63))False)False)(∀ x63 . (x62 x63False)x62 (x46 x63)False)(∀ x63 . (x62 x63False)(x2 (x46 x63) (x1 x63)False)False)((x24 x45False)False)(x62 x45False)((x55 x44False)False)(x62 x44False)(∀ x63 . x8 x63x60 x63(x53 (x43 x63) x63False)False)(∀ x63 . x8 x63x60 x63(x2 (x43 x63) (x1 (x57 x63))False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))(x5 x64 (x5 x64 x63) = x5 x64 x63False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))(x59 x64 (x59 x64 x63) = x59 x64 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x58 x65 x64 x64 = x64False)False)(∀ x63 . (x4 x63 x63 = x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))(x53 (x59 x64 x63) x64False)False)(∀ x63 x64 x65 . x8 x65x60 x65x53 x64 x65x2 x64 (x1 (x57 x65))x53 x63 x65x2 x63 (x1 (x57 x65))(x53 (x4 x64 x63) x65False)False)(∀ x63 x64 . (x62 x64False)x62 (x4 x63 x64)False)(∀ x63 x64 x65 . x8 x65x60 x65x11 x64 x65x2 x64 (x1 (x57 x65))x11 x63 x65x2 x63 (x1 (x57 x65))(x11 (x4 x64 x63) x65False)False)(∀ x63 x64 . (x62 x64False)x62 (x4 x64 x63)False)(∀ x63 x64 . x24 x64x24 x63(x24 (x4 x64 x63)False)False)(∀ x63 x64 . x55 x64x55 x63(x55 (x4 x64 x63)False)False)(∀ x63 x64 . x26 x64x26 x63(x26 (x4 x64 x63)False)False)(∀ x63 x64 . x42 x64x42 x63(x42 (x4 x64 x63)False)False)(∀ x63 x64 . x27 x64x27 x63(x27 (x4 x64 x63)False)False)(∀ x63 x64 . x41 x64x41 x63(x41 (x4 x64 x63)False)False)(∀ x63 x64 . x28 x64x28 x63(x28 (x4 x64 x63)False)False)((x62 x61False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))(x11 (x5 x64 x63) x64False)False)(∀ x63 . x62 (x1 x63)False)(∀ x63 x64 . x60 x64x14 x63 x64x2 x63 (x1 (x57 x64))(x62 (x59 x64 x63)False)False)(∀ x63 . (x2 (x40 x63) x63False)False)((x29 x30False)False)((x60 x39False)False)(∀ x63 . x60 x63(x29 x63False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x2 (x58 x65 x64 x63) (x1 x65)False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))(x2 (x5 x64 x63) (x1 (x57 x64))False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))(x2 (x59 x64 x63) (x1 (x57 x64))False)False)(∀ x63 x64 x65 . x2 x64 (x1 x65)x2 x63 (x1 x65)(x58 x65 x64 x63 = x58 x65 x63 x64False)False)(∀ x63 x64 . (x4 x64 x63 = x4 x63 x64False)False)(∀ x63 . x6 x63(x31 x63False)False)(∀ x63 . x62 x63(x6 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x53 x63 x64x9 x63 x64(x62 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x11 x63 x64x14 x63 x64(x9 x63 x64False)False)(∀ x63 . x27 x63(x28 x63False)False)(∀ x63 . x15 x63(x56 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x9 x63 x64(x14 x63 x64False)False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)x19 x63 x64False)(∀ x63 . x62 x63x24 x63(x51 x63False)False)(∀ x63 . x62 x63x24 x63(x24 x63False)False)(∀ x63 . x27 x63(x41 x63False)False)(∀ x63 . x24 x63x62 x63(x38 x63False)False)(∀ x63 . x24 x63x62 x63(x24 x63False)False)(∀ x63 . x15 x63(x17 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x62 x63(x9 x63 x64False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)x62 x63(x19 x63 x64False)False)(∀ x63 . x62 x63x24 x63(x32 x63False)False)(∀ x63 . x62 x63x24 x63(x24 x63False)False)(∀ x63 . x42 x63(x27 x63False)False)(∀ x63 . x37 x63(x15 x63False)False)(∀ x63 x64 . x60 x64x2 x63 (x1 (x57 x64))x62 x63(x14 x63 x64False)False)(∀ x63 x64 . (x62 x64False)x2 x63 (x1 x64)(x19 x63 x64False)x62 x63False)(∀ x63 x64 . x24 x64x2 x63 (x1 x64)(x24 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x62 x63(x11 x63 x64False)False)(∀ x63 . x26 x63(x42 x63False)False)(∀ x63 . x62 x63(x21 x63False)False)(∀ x63 x64 . x55 x64x2 x63 (x1 x64)(x55 x63False)False)(∀ x63 x64 . x26 x64x2 x63 (x1 x64)(x26 x63False)False)(∀ x63 x64 . x42 x64x2 x63 (x1 x64)(x42 x63False)False)(∀ x63 x64 . x27 x64x2 x63 (x1 x64)(x27 x63False)False)(∀ x63 x64 . x41 x64x2 x63 (x1 x64)(x41 x63False)False)(∀ x63 x64 . x8 x64x60 x64x2 x63 (x1 (x57 x64))x62 x63(x53 x63 x64False)False)(∀ x63 x64 . x62 x64x2 x63 (x1 x64)(x62 x63False)False)(∀ x63 . x62 x63(x24 x63False)False)(∀ x63 . x55 x63(x26 x63False)False)(∀ x63 . x24 x63x62 x63(x38 x63False)False)(∀ x63 . x24 x63x62 x63(x24 x63False)False)(∀ x63 x64 . x28 x64x2 x63 (x1 x64)(x28 x63False)False)(∀ x63 . x62 x63(x55 x63False)False)(∀ x63 x64 . x55 x64x2 x63 x64(x37 x63False)False)(∀ x63 x64 . x26 x64x2 x63 x64(x33 x63False)False)(∀ x63 x64 . x42 x64x2 x63 x64(x36 x63False)False)(∀ x63 x64 . x27 x64x2 x63 x64(x15 x63False)False)(∀ x63 x64 . x41 x64x2 x63 x64(x56 x63False)False)(∀ x63 x64 . x28 x64x2 x63 x64(x17 x63False)False)(∀ x63 x64 . x6 x64x2 x63 (x1 x64)(x6 x63False)False)(∀ x63 x64 . x6 x64x2 x63 x64(x38 x63False)False)(∀ x63 x64 . x0 x63 x64x0 x64 x63False)(x3 (x58 (x57 x34) x35 (x59 x34 (x5 x34 x35))) (x5 x34 (x59 x34 (x58 (x57 x34) x35 (x59 x34 (x5 x34 x35)))))False)((x3 x35 (x5 x34 (x59 x34 x35))False)False)((x2 x35 (x1 (x57 x34))False)False)((x60 x34False)False)((x8 x34False)False)False (proof)