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Proofgold Signed Transaction

vin
PrFwu../06ecb..
PURaT../376f6..
vout
PrFwu../47ec7.. 24.91 bars
TMTGQ../51111.. ownership of ef99f.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMMXk../4b73e.. ownership of 70a03.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMG5d../72a31.. ownership of 6922b.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMdAv../f1844.. ownership of 08918.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMSc6../92b64.. ownership of 389e6.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMKX8../66ef6.. ownership of 333ed.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
PUg44../4802e.. doc published by PrGM6..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Definition 2f869.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2∀ x6 : ο . x6)(x1 = x3∀ x6 : ο . x6)(x2 = x3∀ x6 : ο . x6)(x1 = x4∀ x6 : ο . x6)(x2 = x4∀ x6 : ο . x6)(x3 = x4∀ x6 : ο . x6)not (x0 x1 x2)not (x0 x1 x3)not (x0 x2 x3)not (x0 x1 x4)not (x0 x2 x4)x0 x3 x4x5)x5
Definition 5a3b5.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (2f869.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)x0 x2 x5not (x0 x3 x5)not (x0 x4 x5)x6)x6
Definition 247da.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (5a3b5.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6not (x0 x2 x6)not (x0 x3 x6)not (x0 x4 x6)x0 x5 x6x7)x7
Definition 87c36.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (2f869.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)x0 x2 x5not (x0 x3 x5)x0 x4 x5x6)x6
Definition 6648a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (87c36.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)not (x0 x1 x6)x0 x2 x6x0 x3 x6not (x0 x4 x6)not (x0 x5 x6)x7)x7
Definition c9184.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (6648a.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7not (x0 x2 x7)not (x0 x3 x7)not (x0 x4 x7)not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition SubqSubq := λ x0 x1 . ∀ x2 . x2x0x2x1
Param atleastpatleastp : ιιο
Definition cdfa5.. := λ x0 x1 . λ x2 : ι → ι → ο . ∀ x3 . x3x1atleastp x0 x3not (∀ x4 . x4x3∀ x5 . x5x3(x4 = x5∀ x6 : ο . x6)x2 x4 x5)
Param u4 : ι
Definition 86706.. := cdfa5.. u4
Definition 35fb6.. := λ x0 . λ x1 : ι → ι → ο . 86706.. x0 (λ x2 x3 . not (x1 x2 x3))
Param SetAdjoinSetAdjoin : ιιι
Param UPairUPair : ιιι
Definition oror := λ x0 x1 : ο . ∀ x2 : ο . (x0x2)(x1x2)x2
Known xmxm : ∀ x0 : ο . or x0 (not x0)
Known dnegdneg : ∀ x0 : ο . not (not x0)x0
Param equipequip : ιιο
Known equip_atleastpequip_atleastp : ∀ x0 x1 . equip x0 x1atleastp x0 x1
Known 7204a.. : ∀ x0 x1 x2 x3 . (x0 = x1∀ x4 : ο . x4)(x0 = x2∀ x4 : ο . x4)(x1 = x2∀ x4 : ο . x4)(x0 = x3∀ x4 : ο . x4)(x1 = x3∀ x4 : ο . x4)(x2 = x3∀ x4 : ο . x4)equip u4 (SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3)
Known 58c12.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 x3 x4 . x0 x1 x2x0 x1 x3x0 x1 x4x0 x2 x3x0 x2 x4x0 x3 x4(∀ x5 . x5SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4∀ x6 . x6SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4x0 x5 x6x0 x6 x5)∀ x5 . x5SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4∀ x6 . x6SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4(x5 = x6∀ x7 : ο . x7)x0 x5 x6
Known c88f0.. : ∀ x0 x1 . x1x0∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4x0
Theorem 389e6.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2x1∀ x3 . x3x1∀ x4 . x4x1∀ x5 . x5x1∀ x6 . x6x1∀ x7 . x7x1∀ x8 . x8x1∀ x9 . x9x1∀ x10 . x10x1∀ x11 . x11x1∀ x12 . x12x1∀ x13 . x13x1∀ x14 . x14x1(∀ x15 . x15x1∀ x16 . x16x1x0 x15 x16x0 x16 x15)(x2 = x8∀ x15 : ο . x15)(x3 = x8∀ x15 : ο . x15)(x4 = x8∀ x15 : ο . x15)(x5 = x8∀ x15 : ο . x15)(x6 = x8∀ x15 : ο . x15)(x7 = x8∀ x15 : ο . x15)(x2 = x9∀ x15 : ο . x15)(x3 = x9∀ x15 : ο . x15)(x4 = x9∀ x15 : ο . x15)(x5 = x9∀ x15 : ο . x15)(x6 = x9∀ x15 : ο . x15)(x7 = x9∀ x15 : ο . x15)(x2 = x10∀ x15 : ο . x15)(x3 = x10∀ x15 : ο . x15)(x4 = x10∀ x15 : ο . x15)(x5 = x10∀ x15 : ο . x15)(x6 = x10∀ x15 : ο . x15)(x7 = x10∀ x15 : ο . x15)(x2 = x11∀ x15 : ο . x15)(x3 = x11∀ x15 : ο . x15)(x4 = x11∀ x15 : ο . x15)(x5 = x11∀ x15 : ο . x15)(x6 = x11∀ x15 : ο . x15)(x7 = x11∀ x15 : ο . x15)(x2 = x12∀ x15 : ο . x15)(x3 = x12∀ x15 : ο . x15)(x4 = x12∀ x15 : ο . x15)(x5 = x12∀ x15 : ο . x15)(x6 = x12∀ x15 : ο . x15)(x7 = x12∀ x15 : ο . x15)(x2 = x13∀ x15 : ο . x15)(x3 = x13∀ x15 : ο . x15)(x4 = x13∀ x15 : ο . x15)(x5 = x13∀ x15 : ο . x15)(x6 = x13∀ x15 : ο . x15)(x7 = x13∀ x15 : ο . x15)(x2 = x14∀ x15 : ο . x15)(x3 = x14∀ x15 : ο . x15)(x4 = x14∀ x15 : ο . x15)(x5 = x14∀ x15 : ο . x15)(x6 = x14∀ x15 : ο . x15)(x7 = x14∀ x15 : ο . x15)247da.. x0 x2 x3 x4 x5 x6 x7c9184.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x2 x9not (x0 x2 x10)False)(x0 x2 x8x0 x2 x12not (x0 x2 x10)False)(x0 x2 x8not (x0 x2 x14)False)False
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Known 2634a.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0c9184.. x1 x2 x3 x4 x5 x6 x7 x8c9184.. x1 x2 x4 x6 x3 x7 x5 x8
Theorem 6922b.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2x1∀ x3 . x3x1∀ x4 . x4x1∀ x5 . x5x1∀ x6 . x6x1∀ x7 . x7x1∀ x8 . x8x1∀ x9 . x9x1∀ x10 . x10x1∀ x11 . x11x1∀ x12 . x12x1∀ x13 . x13x1∀ x14 . x14x1(∀ x15 . x15x1∀ x16 . x16x1x0 x15 x16x0 x16 x15)(x2 = x8∀ x15 : ο . x15)(x3 = x8∀ x15 : ο . x15)(x4 = x8∀ x15 : ο . x15)(x5 = x8∀ x15 : ο . x15)(x6 = x8∀ x15 : ο . x15)(x7 = x8∀ x15 : ο . x15)(x2 = x9∀ x15 : ο . x15)(x3 = x9∀ x15 : ο . x15)(x4 = x9∀ x15 : ο . x15)(x5 = x9∀ x15 : ο . x15)(x6 = x9∀ x15 : ο . x15)(x7 = x9∀ x15 : ο . x15)(x2 = x10∀ x15 : ο . x15)(x3 = x10∀ x15 : ο . x15)(x4 = x10∀ x15 : ο . x15)(x5 = x10∀ x15 : ο . x15)(x6 = x10∀ x15 : ο . x15)(x7 = x10∀ x15 : ο . x15)(x2 = x11∀ x15 : ο . x15)(x3 = x11∀ x15 : ο . x15)(x4 = x11∀ x15 : ο . x15)(x5 = x11∀ x15 : ο . x15)(x6 = x11∀ x15 : ο . x15)(x7 = x11∀ x15 : ο . x15)(x2 = x12∀ x15 : ο . x15)(x3 = x12∀ x15 : ο . x15)(x4 = x12∀ x15 : ο . x15)(x5 = x12∀ x15 : ο . x15)(x6 = x12∀ x15 : ο . x15)(x7 = x12∀ x15 : ο . x15)(x2 = x13∀ x15 : ο . x15)(x3 = x13∀ x15 : ο . x15)(x4 = x13∀ x15 : ο . x15)(x5 = x13∀ x15 : ο . x15)(x6 = x13∀ x15 : ο . x15)(x7 = x13∀ x15 : ο . x15)(x2 = x14∀ x15 : ο . x15)(x3 = x14∀ x15 : ο . x15)(x4 = x14∀ x15 : ο . x15)(x5 = x14∀ x15 : ο . x15)(x6 = x14∀ x15 : ο . x15)(x7 = x14∀ x15 : ο . x15)247da.. x0 x2 x3 x4 x5 x6 x7c9184.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x2 x8x0 x2 x13not (x0 x2 x12)False)(x0 x2 x8not (x0 x2 x14)False)False
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Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Known 47012.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0c9184.. x1 x2 x3 x4 x5 x6 x7 x8c9184.. x1 x2 x5 x3 x7 x4 x6 x8
Known 268a2.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0c9184.. x1 x2 x3 x4 x5 x6 x7 x8c9184.. x1 x8 x3 x4 x5 x6 x7 x2
Known andIandI : ∀ x0 x1 : ο . x0x1and x0 x1
Known FalseEFalseE : False∀ x0 : ο . x0
Theorem ef99f.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2x1∀ x3 . x3x1∀ x4 . x4x1∀ x5 . x5x1∀ x6 . x6x1∀ x7 . x7x1∀ x8 . x8x1∀ x9 . x9x1∀ x10 . x10x1∀ x11 . x11x1∀ x12 . x12x1∀ x13 . x13x1∀ x14 . x14x1(∀ x15 . x15x1∀ x16 . x16x1x0 x15 x16x0 x16 x15)(x2 = x8∀ x15 : ο . x15)(x3 = x8∀ x15 : ο . x15)(x4 = x8∀ x15 : ο . x15)(x5 = x8∀ x15 : ο . x15)(x6 = x8∀ x15 : ο . x15)(x7 = x8∀ x15 : ο . x15)(x2 = x9∀ x15 : ο . x15)(x3 = x9∀ x15 : ο . x15)(x4 = x9∀ x15 : ο . x15)(x5 = x9∀ x15 : ο . x15)(x6 = x9∀ x15 : ο . x15)(x7 = x9∀ x15 : ο . x15)(x2 = x10∀ x15 : ο . x15)(x3 = x10∀ x15 : ο . x15)(x4 = x10∀ x15 : ο . x15)(x5 = x10∀ x15 : ο . x15)(x6 = x10∀ x15 : ο . x15)(x7 = x10∀ x15 : ο . x15)(x2 = x11∀ x15 : ο . x15)(x3 = x11∀ x15 : ο . x15)(x4 = x11∀ x15 : ο . x15)(x5 = x11∀ x15 : ο . x15)(x6 = x11∀ x15 : ο . x15)(x7 = x11∀ x15 : ο . x15)(x2 = x12∀ x15 : ο . x15)(x3 = x12∀ x15 : ο . x15)(x4 = x12∀ x15 : ο . x15)(x5 = x12∀ x15 : ο . x15)(x6 = x12∀ x15 : ο . x15)(x7 = x12∀ x15 : ο . x15)(x2 = x13∀ x15 : ο . x15)(x3 = x13∀ x15 : ο . x15)(x4 = x13∀ x15 : ο . x15)(x5 = x13∀ x15 : ο . x15)(x6 = x13∀ x15 : ο . x15)(x7 = x13∀ x15 : ο . x15)(x2 = x14∀ x15 : ο . x15)(x3 = x14∀ x15 : ο . x15)(x4 = x14∀ x15 : ο . x15)(x5 = x14∀ x15 : ο . x15)(x6 = x14∀ x15 : ο . x15)(x7 = x14∀ x15 : ο . x15)247da.. x0 x2 x3 x4 x5 x6 x7c9184.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0False
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