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Proofgold Signed Transaction

vin
PrPhD../8e2ca..
PUbbH../13612..
vout
PrPhD../b5316.. 3.40 bars
TMWTj../fdd8f.. ownership of 54bfa.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
TMT6D../ccb4a.. ownership of 4381f.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
PUTeK../13f81.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 54bfa.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ο . ∀ x2 . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 . ∀ x10 : ι → ι → ι → ο . ∀ x11 x12 x13 . ∀ x14 : ι → ο . ∀ x15 . ∀ x16 : ι → ο . ∀ x17 x18 x19 . ∀ x20 : ι → ο . ∀ x21 . ∀ x22 : ι → ο . ∀ x23 x24 x25 x26 . ∀ x27 : ι → ι . ∀ x28 x29 : ι → ι → ι . ∀ x30 x31 : ι → ο . ∀ x32 x33 . ∀ x34 x35 x36 x37 : ι → ο . ∀ x38 : ι → ι . ∀ x39 x40 : ι → ο . ∀ x41 x42 x43 x44 x45 x46 . ∀ x47 : ι → ο . ∀ x48 . ∀ x49 : ι → ο . ∀ x50 . ∀ x51 : ι → ο . ∀ x52 x53 . ∀ x54 x55 : ι → ι . ∀ x56 x57 : ι → ο . ∀ x58 x59 x60 . ∀ x61 x62 : ι → ο . ∀ x63 : ι → ι → ο . ∀ x64 : ι → ο . (∀ x65 x66 . x64 x66x64 x65(x63 x66 x65False)(x62 x65False)(x61 x66False)False)(∀ x65 x66 . x0 x66(x66 = x65False)x0 x65False)(∀ x65 x66 . x64 x66x64 x65(x63 x66 x65False)(x61 x66False)(x62 x65False)False)(∀ x65 x66 . x1 x65 x66x0 x66False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x0 x66False)(x61 x65False)(x62 x66False)False)(∀ x65 x66 . x64 x66x4 x65(x63 x66 x2False)x63 (x3 x66 x65) x2False)(∀ x65 . x0 x65(x65 = x60False)False)(∀ x65 x66 x67 . x1 x65 x66x6 x66 (x5 x67)x0 x67False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x0 x65False)(x62 x66False)(x61 x65False)False)(∀ x65 x66 x67 . x1 x66 x67x6 x67 (x5 x65)(x6 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x61 x65False)x61 x66False)(∀ x65 x66 . x7 x66 x65(x6 x66 (x5 x65)False)False)(∀ x65 x66 . x6 x66 (x5 x65)(x7 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x62 x66False)x62 x65False)(∀ x65 x66 . x6 x65 x66(x0 x66False)(x1 x65 x66False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65x62 x65(x62 x66False)False)(∀ x65 x66 . x1 x66 x65(x6 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65x61 x66(x61 x65False)False)((x6 x60 x59False)False)((x6 x9 x8False)False)((x6 x9 x58False)False)((x10 x9 x8 x58False)False)((x0 x9False)False)((x63 x9 x9False)False)(∀ x65 x66 . x57 x66x57 x65(x63 x66 x66False)False)(∀ x65 . (x7 x65 x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x6 x65 (x5 x67)x6 x66 x65(x10 x66 x67 x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x6 x65 (x5 x67)x10 x66 x67 x65(x6 x66 x65False)False)((x2 = x60False)False)((x58 = x59False)False)(∀ x65 . x56 x65(x54 x65 = x55 x65False)False)((x4 x11False)False)(x0 x11False)((x57 x12False)False)((x0 x12False)False)((x64 x13False)False)((x57 x13False)False)((x14 x13False)False)((x0 x13False)False)((x4 x15False)False)((x62 x53False)False)((x57 x53False)False)((x64 x52False)False)((x62 x52False)False)((x57 x52False)False)((x14 x52False)False)((x51 x50False)False)((x16 x50False)False)(x0 x50False)((x61 x17False)False)((x57 x17False)False)((x64 x18False)False)((x61 x18False)False)((x57 x18False)False)((x14 x18False)False)(x0 x19False)((x49 x48False)False)((x20 x21False)False)((x47 x21False)False)((x22 x21False)False)(x0 x21False)((x20 x23False)False)(x0 x23False)((x6 x23 (x5 x8)False)False)((x16 x46False)False)(x0 x46False)((x56 x45False)False)((x57 x24False)False)((x64 x44False)False)((x0 x25False)False)((x49 x43False)False)((x64 x43False)False)((x14 x43False)False)((x57 x43False)False)((x6 x43 x8False)False)((x20 x26False)False)((x16 x42False)False)(x0 x42False)((x56 x41False)False)((x64 x41False)False)((x14 x41False)False)((x57 x41False)False)((x6 x41 x8False)False)(∀ x65 . x56 x65(x54 (x54 x65) = x54 x65False)False)(∀ x65 . x14 x65(x55 (x55 x65) = x55 x65False)False)(∀ x65 . x14 x65(x27 (x27 x65) = x65False)False)(x40 x8False)(∀ x65 . x49 x65(x49 (x27 x65)False)False)(∀ x65 . x49 x65(x14 (x27 x65)False)False)((x20 x59False)False)(x0 x59False)((x16 x59False)False)((x51 x59False)False)((x51 x8False)False)(∀ x65 . x64 x65(x64 (x27 x65)False)False)(∀ x65 . x64 x65(x14 (x27 x65)False)False)(∀ x65 x66 . x4 x66x4 x65(x4 (x3 x66 x65)False)False)(∀ x65 x66 . x14 x66x4 x65(x14 (x3 x66 x65)False)False)((x39 x8False)False)(∀ x65 . (x62 x65False)x64 x65x62 (x27 x65)False)(∀ x65 . (x62 x65False)x64 x65(x14 (x27 x65)False)False)(∀ x65 x66 . x64 x66x56 x65(x64 (x28 x66 x65)False)False)(∀ x65 x66 . x64 x66x4 x65(x64 (x3 x66 x65)False)False)(∀ x65 . x62 x65x64 x65(x62 (x27 x65)False)False)(∀ x65 . x62 x65x64 x65(x14 (x27 x65)False)False)(∀ x65 . (x61 x65False)x64 x65x61 (x27 x65)False)(∀ x65 . (x61 x65False)x64 x65(x14 (x27 x65)False)False)(∀ x65 . x61 x65x64 x65(x61 (x27 x65)False)False)(∀ x65 . x61 x65x64 x65(x14 (x27 x65)False)False)((x0 x60False)False)(∀ x65 . x49 x65(x49 (x55 x65)False)False)(∀ x65 . x49 x65(x64 (x55 x65)False)False)(∀ x65 . x56 x65(x64 (x55 x65)False)False)(∀ x65 . x56 x65(x4 (x55 x65)False)False)(x0 x8False)(∀ x65 x66 . (x0 x66False)(x0 x65False)x6 x65 (x5 x66)(x10 (x29 x65 x66) x66 x65False)False)(∀ x65 . (x6 (x38 x65) x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x6 x65 (x5 x67)x10 x66 x67 x65(x6 x66 x67False)False)((x10 x2 x8 x58False)False)(∀ x65 . x14 x65(x14 (x27 x65)False)False)((x6 x58 (x5 x8)False)False)(∀ x65 . x56 x65(x6 (x54 x65) x58False)False)(∀ x65 . x14 x65(x64 (x55 x65)False)False)(∀ x65 x66 . x64 x66x56 x65(x63 x2 x65False)(x28 x66 x65 = x27 (x3 x66 (x54 x65))False)False)(∀ x65 x66 . x64 x66x56 x65x63 x2 x65(x28 x66 x65 = x3 x66 (x54 x65)False)False)(∀ x65 x66 . x57 x66x57 x65(x63 x66 x65False)(x63 x65 x66False)False)(∀ x65 . x0 x65(x37 x65False)False)(∀ x65 . x57 x65(x61 x65False)(x62 x65False)(x57 x65False)False)(∀ x65 . x57 x65(x61 x65False)(x62 x65False)(x0 x65False)False)(∀ x65 . x6 x65 x59(x4 x65False)False)(∀ x65 . x6 x65 (x5 x8)(x39 x65False)False)(∀ x65 . x0 x65x57 x65x62 x65False)(∀ x65 . x0 x65x57 x65x61 x65False)(∀ x65 . x0 x65x57 x65(x57 x65False)False)(∀ x65 . x0 x65(x4 x65False)False)(∀ x65 . (x0 x65False)x57 x65(x61 x65False)(x62 x65False)False)(∀ x65 . (x0 x65False)x57 x65(x61 x65False)(x57 x65False)False)(∀ x65 . x4 x65(x20 x65False)False)(∀ x65 . x57 x65x62 x65x61 x65False)(∀ x65 . x57 x65x62 x65(x57 x65False)False)(∀ x65 . x57 x65x62 x65x0 x65False)(∀ x65 x66 . x20 x66x6 x65 x66(x20 x65False)False)(∀ x65 . x39 x65(x36 x65False)False)(∀ x65 . (x0 x65False)x57 x65(x62 x65False)(x61 x65False)False)(∀ x65 . (x0 x65False)x57 x65(x62 x65False)(x57 x65False)False)(∀ x65 . x64 x65(x57 x65False)False)(∀ x65 . x0 x65(x35 x65False)False)(∀ x65 . x39 x65(x30 x65False)False)(∀ x65 . x57 x65x61 x65x62 x65False)(∀ x65 . x57 x65x61 x65(x57 x65False)False)(∀ x65 . x57 x65x61 x65x0 x65False)(∀ x65 . x64 x65(x14 x65False)False)(∀ x65 . x0 x65(x20 x65False)False)(∀ x65 . x4 x65x62 x65False)(∀ x65 . x4 x65(x4 x65False)False)(∀ x65 . x31 x65(x39 x65False)False)(∀ x65 . x56 x65(x64 x65False)False)(∀ x65 . x4 x65(x57 x65False)False)(∀ x65 . x4 x65(x64 x65False)False)(∀ x65 . x56 x65(x49 x65False)False)(∀ x65 . x22 x65x47 x65(x20 x65False)False)(∀ x65 . x6 x65 x58x62 x65False)(∀ x65 . x34 x65(x31 x65False)False)(∀ x65 . x4 x65(x56 x65False)False)(∀ x65 . x0 x65(x51 x65False)False)(∀ x65 . x6 x65 x58(x16 x65False)False)(∀ x65 x66 . x16 x66x6 x65 (x5 x66)(x16 x65False)False)(∀ x65 x66 . x34 x66x6 x65 (x5 x66)(x34 x65False)False)(∀ x65 x66 . x31 x66x6 x65 (x5 x66)(x31 x65False)False)(∀ x65 x66 . x39 x66x6 x65 (x5 x66)(x39 x65False)False)(∀ x65 x66 . x30 x66x6 x65 (x5 x66)(x30 x65False)False)(∀ x65 . x6 x65 x8(x64 x65False)False)(∀ x65 . x49 x65(x64 x65False)False)(∀ x65 . x20 x65(x47 x65False)False)(∀ x65 . x20 x65(x22 x65False)False)(∀ x65 . x4 x65(x4 x65False)False)(∀ x65 . x4 x65(x20 x65False)False)(∀ x65 . x16 x65(x34 x65False)False)(∀ x65 x66 . x36 x66x6 x65 (x5 x66)(x36 x65False)False)(∀ x65 . x0 x65(x16 x65False)False)(∀ x65 x66 . x16 x66x6 x65 x66(x4 x65False)False)(∀ x65 x66 . x34 x66x6 x65 x66(x56 x65False)False)(∀ x65 x66 . x31 x66x6 x65 x66(x49 x65False)False)(∀ x65 x66 . x39 x66x6 x65 x66(x64 x65False)False)(∀ x65 x66 . x30 x66x6 x65 x66(x57 x65False)False)(∀ x65 x66 . x36 x66x6 x65 x66(x14 x65False)False)(∀ x65 . x6 x65 (x5 x58)(x16 x65False)False)(∀ x65 x66 . x37 x66x6 x65 (x5 x66)(x37 x65False)False)(∀ x65 x66 . x1 x65 x66x1 x66 x65False)((x63 (x28 x33 x32) x2False)False)(x63 x33 x2False)((x56 x32False)False)((x64 x33False)False)False (proof)