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Proofgold Signed Transaction

vin
PrNUD../f4da2..
PUdgk../9d7e1..
vout
PrNUD../e3c0d.. 0.04 bars
TMYv2../19df2.. ownership of e1852.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
TMdfw../8bb2c.. ownership of 427c3.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
PUYKK../3c6ae.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem e1852.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . ∀ x8 : ι → ι → ι → ο . ∀ x9 : ι → ι → ι . ∀ x10 : ι → ο . ∀ x11 x12 : ι → ι . ∀ x13 : ι → ο . ∀ x14 x15 . ∀ x16 : ι → ο . ∀ x17 x18 . ∀ x19 : ι → ο . ∀ x20 x21 x22 x23 x24 . ∀ x25 x26 : ι → ι → ι . ∀ x27 : ι → ο . ∀ x28 : ι → ι . ∀ x29 x30 x31 x32 : ι → ι → ι → ι . ∀ x33 x34 x35 x36 : ι → ο . ∀ x37 x38 x39 . ∀ x40 x41 : ι → ο . ∀ x42 : ι → ι → ι . ∀ x43 : ι → ο . ∀ x44 . ∀ x45 : ι → ο . ∀ x46 x47 x48 x49 x50 x51 . ∀ x52 : ι → ο . ∀ x53 x54 : ι → ι . ∀ x55 x56 . ∀ x57 : ι → ο . ∀ x58 . ∀ x59 : ι → ι → ι . ∀ x60 : 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 . x0 x65 x64(x2 x65 x64False)False)((x2 x62 x4False)False)(∀ x64 x65 . x61 x65x61 x64(x59 (x60 x65) (x60 x64) = x59 x64 x65False)False)(∀ x64 x65 . x61 x65x61 x64(x5 (x60 x65) (x60 x64) = x60 (x5 x65 x64)False)False)(∀ x64 x65 x66 . x61 x66x61 x64x61 x65(x5 (x5 x66 x64) x65 = x5 x66 (x5 x64 x65)False)False)((x2 x7 x6False)False)((x2 x7 x58False)False)((x8 x7 x6 x58False)False)((x57 x7False)False)(x63 x7False)((x2 x56 x6False)False)((x2 x56 x58False)False)((x8 x56 x6 x58False)False)((x57 x56False)False)(x63 x56False)(∀ x64 x65 . x61 x65x61 x64(x5 x65 (x60 x64) = x59 x65 x64False)False)((x2 x55 x6False)False)((x2 x55 x58False)False)((x8 x55 x6 x58False)False)((x63 x55False)False)((x60 (x60 x7) = x7False)False)((x60 (x60 x56) = x56False)False)((x60 x7 = x60 x7False)False)((x60 x56 = x60 x56False)False)((x60 x55 = x55False)False)((x59 (x60 x7) (x60 x7) = x55False)False)((x59 (x60 x7) (x60 x56) = x60 x56False)False)((x59 (x60 x7) x55 = x60 x7False)False)((x59 (x60 x56) (x60 x7) = x56False)False)((x59 (x60 x56) (x60 x56) = x55False)False)((x59 (x60 x56) x56 = x60 x7False)False)((x59 (x60 x56) x55 = x60 x56False)False)((x59 x7 x7 = x55False)False)((x59 x7 x56 = x56False)False)((x59 x7 x55 = x7False)False)((x59 x56 (x60 x56) = x7False)False)((x59 x56 x7 = x60 x56False)False)((x59 x56 x56 = x55False)False)((x59 x56 x55 = x56False)False)((x59 x55 (x60 x7) = x7False)False)((x59 x55 (x60 x56) = x56False)False)((x59 x55 x7 = x60 x7False)False)((x59 x55 x56 = x60 x56False)False)((x59 x55 x55 = x55False)False)((x5 (x60 x7) x7 = x55False)False)((x5 (x60 x7) x56 = x60 x56False)False)((x5 (x60 x56) (x60 x56) = x60 x7False)False)((x5 (x60 x56) x7 = x56False)False)((x5 (x60 x56) x56 = x55False)False)((x5 (x60 x56) x55 = x60 x56False)False)((x5 x7 (x60 x7) = x55False)False)((x5 x7 (x60 x56) = x56False)False)((x5 x7 x55 = x7False)False)((x5 x56 (x60 x7) = x60 x56False)False)((x5 x56 (x60 x56) = x55False)False)((x5 x56 x56 = x7False)False)((x5 x56 x55 = x56False)False)((x5 x55 (x60 x7) = x60 x7False)False)((x5 x55 (x60 x56) = x60 x56False)False)((x5 x55 x7 = x7False)False)((x5 x55 x56 = x56False)False)((x5 x55 x55 = x55False)False)(∀ x64 . (x3 x64 x64False)False)(∀ x64 x65 x66 . (x63 x66False)(x63 x64False)x2 x64 (x1 x66)x2 x65 x64(x8 x65 x66 x64False)False)(∀ x64 x65 x66 . (x63 x66False)(x63 x64False)x2 x64 (x1 x66)x8 x65 x66 x64(x2 x65 x64False)False)(∀ x64 x65 . x2 x65 x6x10 x64(x9 x65 x64 = x5 x65 x64False)False)((x58 = x4False)False)(∀ x64 . x61 x64(x12 x64 = x11 x64False)False)(∀ x64 . x61 x64(x53 x64 = x54 x64False)False)((x13 x14False)False)((x63 x14False)False)((x10 x15False)False)((x13 x15False)False)((x61 x15False)False)((x63 x15False)False)((x16 x17False)False)((x13 x17False)False)((x10 x18False)False)((x16 x18False)False)((x13 x18False)False)((x61 x18False)False)((x19 x20False)False)((x52 x20False)False)(x63 x20False)((x57 x51False)False)((x13 x51False)False)((x10 x50False)False)((x57 x50False)False)((x13 x50False)False)((x61 x50False)False)((x61 x49False)False)(x63 x49False)(x63 x48False)((x52 x21False)False)(x63 x21False)((x13 x22False)False)((x10 x47False)False)((x61 x23False)False)((x63 x46False)False)((x52 x24False)False)(x63 x24False)(∀ x64 x65 . x2 x65 x6x2 x64 x6(x12 (x25 x65 x64) = x64False)False)(∀ x64 x65 . x2 x65 x6x2 x64 x6(x53 (x25 x65 x64) = x65False)False)(∀ x64 x65 x66 x67 . x2 x67 x6x2 x64 x6x10 x66x10 x65x67 = x66x64 = x65(x26 x67 x64 = x5 x66 x65False)False)(∀ x64 . x61 x64(x60 (x60 x64) = x64False)False)(∀ x64 x65 . (x16 x65False)x10 x65(x16 x64False)x10 x64x16 (x5 x65 x64)False)(x45 x44False)(x45 x6False)(∀ x64 x65 . x10 x65x10 x64(x10 (x59 x65 x64)False)False)(∀ x64 . (x63 x64False)x61 x64(x61 (x60 x64)False)False)(∀ x64 . (x63 x64False)x61 x64x63 (x60 x64)False)((x52 x4False)False)(∀ x64 x65 . x10 x65x10 x64(x10 (x5 x65 x64)False)False)((x19 x4False)False)((x19 x6False)False)((x19 x44False)False)(∀ x64 x65 . x61 x65x61 x64(x61 (x59 x65 x64)False)False)(∀ x64 . x10 x64(x10 (x60 x64)False)False)(∀ x64 . x10 x64(x61 (x60 x64)False)False)((x27 x6False)False)(∀ x64 x65 . x61 x65x61 x64(x61 (x5 x65 x64)False)False)(x63 x44False)(∀ x64 . x61 x64(x10 (x11 x64)False)False)(∀ x64 x65 . x16 x65x10 x65(x16 x64False)x10 x64(x57 (x59 x64 x65)False)False)(∀ x64 x65 . x16 x65x10 x65(x16 x64False)x10 x64(x16 (x59 x65 x64)False)False)(∀ x64 x65 . x57 x65x10 x65(x57 x64False)x10 x64(x16 (x59 x64 x65)False)False)((x63 x62False)False)(x63 x6False)((x43 x44False)False)(∀ x64 . x61 x64(x10 (x54 x64)False)False)(∀ x64 x65 . x57 x65x10 x65(x57 x64False)x10 x64(x57 (x59 x65 x64)False)False)(∀ x64 x65 . (x16 x65False)x10 x65(x57 x64False)x10 x64x57 (x59 x64 x65)False)(∀ x64 x65 . (x16 x65False)x10 x65(x57 x64False)x10 x64x16 (x59 x65 x64)False)(∀ x64 . (x16 x64False)x10 x64x57 (x60 x64)False)(∀ x64 . (x16 x64False)x10 x64(x61 (x60 x64)False)False)(∀ x64 . (x57 x64False)x10 x64x16 (x60 x64)False)(∀ x64 . (x57 x64False)x10 x64(x61 (x60 x64)False)False)(∀ x64 x65 . x16 x65x10 x65(x57 x64False)x10 x64(x16 (x5 x64 x65)False)False)(∀ x64 x65 . x16 x65x10 x65(x57 x64False)x10 x64(x16 (x5 x65 x64)False)False)(∀ x64 x65 . x57 x65x10 x65(x16 x64False)x10 x64(x57 (x5 x64 x65)False)False)(∀ x64 x65 . x57 x65x10 x65(x16 x64False)x10 x64(x57 (x5 x65 x64)False)False)(∀ x64 x65 . (x57 x65False)x10 x65(x57 x64False)x10 x64x57 (x5 x65 x64)False)(∀ x64 x65 . (x63 x65False)(x63 x64False)x2 x64 (x1 x65)(x8 (x42 x64 x65) x65 x64False)False)(∀ x64 . (x2 (x28 x64) x64False)False)(∀ x64 x65 x66 . (x63 x66False)(x63 x64False)x2 x64 (x1 x66)x8 x65 x66 x64(x2 x65 x66False)False)(∀ x64 x65 . x2 x65 x6x10 x64(x2 (x9 x65 x64) x6False)False)((x2 x58 (x1 x6)False)False)(∀ x64 x65 . x2 x65 x6x2 x64 x6(x2 (x25 x65 x64) x44False)False)(∀ x64 . x61 x64(x61 (x60 x64)False)False)(∀ x64 . x61 x64(x2 (x12 x64) x6False)False)(∀ x64 . x61 x64(x2 (x53 x64) x6False)False)(∀ x64 x65 . x2 x65 x6x2 x64 x6(x2 (x26 x65 x64) x6False)False)(∀ x64 x65 x66 x67 x68 x69 x70 . x61 x70x61 x64x2 x69 x6x2 x65 x6x2 x68 x6x2 x66 x6x70 = x25 x69 x65x64 = x25 x68 x66x67 = x25 (x26 x69 x68) (x26 x65 x66)(x67 = x5 x70 x64False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x65 = x25 (x26 (x29 x65 x64 x66) (x30 x65 x64 x66)) (x26 (x31 x65 x64 x66) (x32 x65 x64 x66))False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x64 = x25 (x30 x65 x64 x66) (x32 x65 x64 x66)False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x66 = x25 (x29 x65 x64 x66) (x31 x65 x64 x66)False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x2 (x32 x65 x64 x66) x6False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x2 (x30 x65 x64 x66) x6False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x2 (x31 x65 x64 x66) x6False)False)(∀ x64 x65 x66 . x61 x66x61 x64x65 = x5 x66 x64(x2 (x29 x65 x64 x66) x6False)False)(∀ x64 x65 . x2 x65 x6x10 x64(x9 x65 x64 = x9 x64 x65False)False)(∀ x64 x65 . x61 x65x61 x64(x5 x65 x64 = x5 x64 x65False)False)(∀ x64 x65 . x2 x65 x6x2 x64 x6(x26 x65 x64 = x26 x64 x65False)False)(∀ x64 . x13 x64(x57 x64False)(x16 x64False)(x13 x64False)False)(∀ x64 . x13 x64(x57 x64False)(x16 x64False)(x63 x64False)False)(∀ x64 . x2 x64 (x1 x6)(x27 x64False)False)(∀ x64 . x63 x64x13 x64x16 x64False)(∀ x64 . x63 x64x13 x64x57 x64False)(∀ x64 . x63 x64x13 x64(x13 x64False)False)(∀ x64 . (x63 x64False)x13 x64(x57 x64False)(x16 x64False)False)(∀ x64 . (x63 x64False)x13 x64(x57 x64False)(x13 x64False)False)(∀ x64 . x2 x64 (x1 x44)(x43 x64False)False)(∀ x64 . x13 x64x16 x64x57 x64False)(∀ x64 . x13 x64x16 x64(x13 x64False)False)(∀ x64 . x13 x64x16 x64x63 x64False)(∀ x64 . x27 x64(x43 x64False)False)(∀ x64 . (x63 x64False)x13 x64(x16 x64False)(x57 x64False)False)(∀ x64 . (x63 x64False)x13 x64(x16 x64False)(x13 x64False)False)(∀ x64 . x10 x64(x13 x64False)False)(∀ x64 . x27 x64(x33 x64False)False)(∀ x64 . x13 x64x57 x64x16 x64False)(∀ x64 . x13 x64x57 x64(x13 x64False)False)(∀ x64 . x13 x64x57 x64x63 x64False)(∀ x64 . x10 x64(x61 x64False)False)(∀ x64 . x2 x64 x44(x61 x64False)False)(∀ x64 . x34 x64(x27 x64False)False)(∀ x64 . x41 x64(x13 x64False)False)(∀ x64 . x41 x64(x10 x64False)False)(∀ x64 . x41 x64(x61 x64False)False)(∀ x64 . x35 x64(x34 x64False)False)(∀ x64 . x63 x64(x19 x64False)False)(∀ x64 . x2 x64 x58(x52 x64False)False)(∀ x64 x65 . x52 x65x2 x64 (x1 x65)(x52 x64False)False)(∀ x64 x65 . x35 x65x2 x64 (x1 x65)(x35 x64False)False)(∀ x64 x65 . x34 x65x2 x64 (x1 x65)(x34 x64False)False)(∀ x64 x65 . x27 x65x2 x64 (x1 x65)(x27 x64False)False)(∀ x64 x65 . x33 x65x2 x64 (x1 x65)(x33 x64False)False)(∀ x64 . x2 x64 x6(x10 x64False)False)(∀ x64 . x2 x64 x6(x61 x64False)False)(∀ x64 . x52 x64(x35 x64False)False)(∀ x64 x65 . x43 x65x2 x64 (x1 x65)(x43 x64False)False)(∀ x64 . x63 x64(x52 x64False)False)(∀ x64 x65 . x52 x65x2 x64 x65(x41 x64False)False)(∀ x64 x65 . x35 x65x2 x64 x65(x36 x64False)False)(∀ x64 x65 . x34 x65x2 x64 x65(x40 x64False)False)(∀ x64 x65 . x27 x65x2 x64 x65(x10 x64False)False)(∀ x64 x65 . x33 x65x2 x64 x65(x13 x64False)False)(∀ x64 x65 . x43 x65x2 x64 x65(x61 x64False)False)(∀ x64 . x2 x64 (x1 x58)(x52 x64False)False)(∀ x64 x65 . x0 x64 x65x0 x65 x64False)(x12 x39 = x9 (x12 x37) (x12 x38)False)((x39 = x5 x37 x38False)False)((x61 x39False)False)((x61 x38False)False)((x61 x37False)False)False (proof)