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Proofgold Signed Transaction

vin
PrAcR../c45b8..
PUYAF../ee5df..
vout
PrAcR../83880.. 24.98 bars
TMWhc../e60aa.. ownership of 659aa.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMZCN../55c57.. ownership of 7254a.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMK1D../38317.. ownership of 1602f.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMcLK../c9ad7.. ownership of ba445.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMMQ9../27b26.. ownership of 9b466.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMMbC../cba29.. ownership of 99385.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMZwy../7d9dd.. ownership of 6d2d7.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMaLX../f9210.. ownership of 3755b.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMLeN../313bb.. ownership of ba104.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMHoe../fd60c.. ownership of c6770.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMXht../8536b.. ownership of aaf99.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMZeb../95663.. ownership of 28b31.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMNx3../01d96.. ownership of c7001.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMWaP../99a55.. ownership of e51e0.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMb3T../1c7a9.. ownership of 6d515.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
TMc1B../e6b12.. ownership of 1a222.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0
PUh1S../c8433.. 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 00e19.. := 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)not (x0 x5 x6)x7)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 f201d.. := 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)x0 x1 x6not (x0 x2 x6)x0 x3 x6not (x0 x4 x6)x0 x5 x6x7)x7
Definition 2452c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f201d.. 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 x7x0 x2 x7not (x0 x3 x7)x0 x4 x7not (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 6d515.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x2 x13x0 x2 x14not (x0 x2 x10)not (x0 x2 x9)x0 x2 x11x0 x2 x12x0 x3 x10not (x0 x3 x9)False)(not (x0 x2 x9)not (x0 x2 x10)x0 x2 x12not (x0 x2 x11)False)(x0 x6 x8not (x0 x3 x8)False)(x0 x6 x8not (x0 x2 x8)False)(x0 x5 x8not (x0 x4 x8)False)(x0 x4 x8not (x0 x3 x8)False)(x0 x4 x8not (x0 x2 x8)False)(x0 x2 x10not (x0 x2 x9)False)False
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Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Known FalseEFalseE : False∀ x0 : ο . x0
Known c75bf.. : ∀ 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 . x8x02452c.. x1 x2 x3 x4 x5 x6 x7 x82452c.. x1 x2 x4 x3 x6 x5 x8 x7
Known and3Iand3I : ∀ x0 x1 x2 : ο . x0x1x2and (and x0 x1) x2
Theorem c7001.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x6 x8not (x0 x3 x8)False)(x0 x6 x8not (x0 x2 x8)False)(x0 x5 x8not (x0 x4 x8)False)(x0 x4 x8not (x0 x3 x8)False)(x0 x4 x8not (x0 x2 x8)False)False
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Known 9d6b5.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x4 x2 x3 x6 x7 x5
Known bd69a.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x2 x4 x6 x3 x5 x7
Theorem aaf99.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x6 x2 x4 x5 x7 x3
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Known 32906.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x2 x6 x4 x5 x3 x7
Theorem ba104.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x5 x8not (x0 x4 x8)False)(x0 x4 x8not (x0 x2 x8)False)(x0 x3 x8not (x0 x2 x8)False)(x0 x4 x8not (x0 x6 x8)False)False
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Known ade0a.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x6 x4 x2 x7 x5 x3
Known andIandI : ∀ x0 x1 : ο . x0x1and x0 x1
Theorem 6d2d7.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x7 x8not (x0 x2 x8)False)(x0 x2 x8not (x0 x6 x8)False)(x0 x4 x8not (x0 x6 x8)False)False
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Theorem 9b466.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x3 x8not (x0 x6 x8)False)(x0 x4 x8not (x0 x7 x8)False)False
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Theorem 1602f.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0(x0 x4 x8not (x0 x7 x8)False)False
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Known d678f.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x000e19.. x1 x2 x3 x4 x5 x6 x700e19.. x1 x4 x6 x7 x2 x3 x5
Theorem 659aa.. : ∀ 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)00e19.. x0 x2 x3 x4 x5 x6 x72452c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x1486706.. x1 x035fb6.. x1 x0False
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