TSTP Solution File: NUM625+3 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM625+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:49:03 EDT 2023
% Result : Theorem 19.84s 3.49s
% Output : Proof 45.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM625+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 14:16:47 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.58 ________ _____
% 0.17/0.58 ___ __ \_________(_)________________________________
% 0.17/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.58
% 0.17/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.58 (2023-06-19)
% 0.17/0.58
% 0.17/0.58 (c) Philipp Rümmer, 2009-2023
% 0.17/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.58 Amanda Stjerna.
% 0.17/0.58 Free software under BSD-3-Clause.
% 0.17/0.58
% 0.17/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.58
% 0.17/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.59 Running up to 7 provers in parallel.
% 0.17/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.17/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 7.59/1.84 Prover 1: Preprocessing ...
% 7.59/1.84 Prover 4: Preprocessing ...
% 7.59/1.89 Prover 2: Preprocessing ...
% 7.59/1.89 Prover 3: Preprocessing ...
% 7.59/1.89 Prover 6: Preprocessing ...
% 7.59/1.89 Prover 0: Preprocessing ...
% 7.59/1.90 Prover 5: Preprocessing ...
% 18.62/3.44 Prover 3: Constructing countermodel ...
% 19.84/3.48 Prover 3: proved (2874ms)
% 19.84/3.48
% 19.84/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.84/3.49
% 19.84/3.49 Prover 2: stopped
% 19.84/3.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.84/3.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.87/3.64 Prover 6: Constructing countermodel ...
% 20.87/3.64 Prover 6: stopped
% 21.35/3.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.27/3.82 Prover 7: Preprocessing ...
% 22.56/3.88 Prover 8: Preprocessing ...
% 23.13/3.97 Prover 0: stopped
% 23.13/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.13/4.08 Prover 10: Preprocessing ...
% 27.36/4.49 Prover 11: Preprocessing ...
% 28.73/4.81 Prover 1: Constructing countermodel ...
% 29.90/4.89 Prover 5: Constructing countermodel ...
% 29.90/4.89 Prover 5: stopped
% 30.44/4.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 31.55/5.08 Prover 8: Warning: ignoring some quantifiers
% 32.28/5.15 Prover 8: Constructing countermodel ...
% 32.28/5.18 Prover 13: Preprocessing ...
% 34.78/5.57 Prover 1: Found proof (size 16)
% 34.78/5.57 Prover 1: proved (4961ms)
% 34.78/5.57 Prover 11: stopped
% 34.78/5.57 Prover 8: stopped
% 34.78/5.57 Prover 13: stopped
% 36.62/5.75 Prover 10: Constructing countermodel ...
% 36.62/5.77 Prover 10: stopped
% 37.18/5.87 Prover 7: Constructing countermodel ...
% 37.18/5.89 Prover 7: stopped
% 45.65/7.94 Prover 4: Constructing countermodel ...
% 45.91/8.03 Prover 4: stopped
% 45.91/8.03
% 45.91/8.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.91/8.03
% 45.91/8.03 % SZS output start Proof for theBenchmark
% 45.91/8.04 Assumptions after simplification:
% 45.91/8.04 ---------------------------------
% 45.91/8.04
% 45.91/8.04 (m__5147)
% 45.91/8.07 szmzizndt0(xQ) = xp & aElementOf0(xp, xQ) = 0 & $i(xp) & $i(xQ) & ! [v0: $i]
% 45.91/8.07 : ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(xp, v0) = v1) | ~ $i(v0) | ? [v2:
% 45.91/8.07 int] : ( ~ (v2 = 0) & aElementOf0(v0, xQ) = v2))
% 45.91/8.07
% 45.91/8.07 (m__5164)
% 45.91/8.08 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 45.91/8.08 aSet0(xP) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 45.91/8.08 (aElementOf0(v1, xP) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 45.91/8.08 (aElement0(v1) = v3 & aElementOf0(v1, xQ) = v4 & ( ~ (v4 = 0) | ~ (v3 =
% 45.91/8.08 0)))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0,
% 45.91/8.08 v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1,
% 45.91/8.08 xQ) = v3)) & ! [v1: $i] : ( ~ (aElementOf0(v1, xP) = 0) | ~ $i(v1) |
% 45.91/8.08 ( ~ (v1 = v0) & aElement0(v1) = 0 & aElementOf0(v1, xQ) = 0)))
% 45.91/8.08
% 45.91/8.08 (m__5348)
% 45.91/8.08 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 &
% 45.91/8.08 aElement0(xx) = 0 & aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 &
% 45.91/8.08 $i(v0))
% 45.91/8.08
% 45.91/8.08 (m__5496)
% 45.91/8.08 xx = xp & $i(xp)
% 45.91/8.08
% 45.91/8.08 (function-axioms)
% 45.91/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.91/8.10 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 45.91/8.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 45.91/8.10 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 45.91/8.10 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 45.91/8.10 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 45.91/8.10 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 45.91/8.10 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 45.91/8.10 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.91/8.10 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 45.91/8.10 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 45.91/8.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.91/8.10 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 45.91/8.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 45.91/8.10 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.91/8.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.91/8.10 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 45.91/8.10 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 45.91/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 45.91/8.10 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.91/8.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 45.91/8.10 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 45.91/8.10 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 45.91/8.10 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 45.91/8.10 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 45.91/8.10 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 45.91/8.10 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 45.91/8.10 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 45.91/8.10 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 45.91/8.10 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 45.91/8.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 45.91/8.10 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 45.91/8.10 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 45.91/8.10 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 45.91/8.10 ~ (aElement0(v2) = v0))
% 45.91/8.10
% 45.91/8.10 Further assumptions not needed in the proof:
% 45.91/8.10 --------------------------------------------
% 45.91/8.10 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 45.91/8.10 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 45.91/8.10 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 45.91/8.10 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 45.91/8.10 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 45.91/8.10 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 45.91/8.10 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 45.91/8.10 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 45.91/8.10 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 45.91/8.10 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__, m__3291, m__3398,
% 45.91/8.10 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 45.91/8.10 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 45.91/8.10 m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106,
% 45.91/8.10 m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, m__5321,
% 45.91/8.10 m__5365, m__5389, m__5401, m__5442, m__5461, m__5481
% 45.91/8.10
% 45.91/8.10 Those formulas are unsatisfiable:
% 45.91/8.10 ---------------------------------
% 45.91/8.10
% 45.91/8.10 Begin of proof
% 45.91/8.10 |
% 45.91/8.10 | ALPHA: (m__5147) implies:
% 45.91/8.10 | (1) szmzizndt0(xQ) = xp
% 45.91/8.10 |
% 45.91/8.10 | ALPHA: (m__5164) implies:
% 45.91/8.11 | (2) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & aSet0(xP)
% 45.91/8.11 | = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 45.91/8.11 | (aElementOf0(v1, xP) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 45.91/8.11 | any] : (aElement0(v1) = v3 & aElementOf0(v1, xQ) = v4 & ( ~ (v4 =
% 45.91/8.11 | 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 45.91/8.11 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 45.91/8.11 | 0) & aElementOf0(v1, xQ) = v3)) & ! [v1: $i] : ( ~
% 45.91/8.11 | (aElementOf0(v1, xP) = 0) | ~ $i(v1) | ( ~ (v1 = v0) &
% 45.91/8.11 | aElement0(v1) = 0 & aElementOf0(v1, xQ) = 0)))
% 45.91/8.11 |
% 45.91/8.11 | ALPHA: (m__5348) implies:
% 45.91/8.11 | (3) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & aElement0(xx) = 0 &
% 45.91/8.11 | aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 & $i(v0))
% 45.91/8.11 |
% 45.91/8.11 | ALPHA: (m__5496) implies:
% 45.91/8.11 | (4) xx = xp
% 45.91/8.11 |
% 45.91/8.11 | ALPHA: (function-axioms) implies:
% 45.91/8.11 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2)
% 45.91/8.11 | = v1) | ~ (szmzizndt0(v2) = v0))
% 45.91/8.11 |
% 45.91/8.11 | DELTA: instantiating (3) with fresh symbol all_94_0 gives:
% 45.91/8.11 | (6) ~ (all_94_0 = xx) & szmzizndt0(xQ) = all_94_0 & aElement0(xx) = 0 &
% 45.91/8.11 | aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 & $i(all_94_0)
% 45.91/8.11 |
% 45.91/8.11 | ALPHA: (6) implies:
% 45.91/8.11 | (7) ~ (all_94_0 = xx)
% 45.91/8.11 | (8) szmzizndt0(xQ) = all_94_0
% 45.91/8.12 |
% 45.91/8.12 | DELTA: instantiating (2) with fresh symbol all_122_0 gives:
% 45.91/8.12 | (9) szmzizndt0(xQ) = all_122_0 & sdtmndt0(xQ, all_122_0) = xP & aSet0(xP) =
% 45.91/8.12 | 0 & $i(all_122_0) & ! [v0: any] : ! [v1: int] : (v1 = 0 | v0 =
% 45.91/8.12 | all_122_0 | ~ (aElementOf0(v0, xP) = v1) | ~ $i(v0) | ? [v2: any]
% 45.91/8.12 | : ? [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0, xQ) = v3 & ( ~
% 45.91/8.12 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 45.91/8.12 | | ~ (sdtlseqdt0(all_122_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 45.91/8.12 | ~ (v2 = 0) & aElementOf0(v0, xQ) = v2)) & ! [v0: $i] : ( ~
% 45.91/8.12 | (aElementOf0(v0, xP) = 0) | ~ $i(v0) | ( ~ (v0 = all_122_0) &
% 45.91/8.12 | aElement0(v0) = 0 & aElementOf0(v0, xQ) = 0))
% 45.91/8.12 |
% 45.91/8.12 | ALPHA: (9) implies:
% 45.91/8.12 | (10) szmzizndt0(xQ) = all_122_0
% 45.91/8.12 |
% 45.91/8.12 | REDUCE: (4), (7) imply:
% 45.91/8.12 | (11) ~ (all_94_0 = xp)
% 45.91/8.12 |
% 45.91/8.12 | GROUND_INST: instantiating (5) with all_94_0, all_122_0, xQ, simplifying with
% 45.91/8.12 | (8), (10) gives:
% 45.91/8.12 | (12) all_122_0 = all_94_0
% 45.91/8.12 |
% 45.91/8.12 | GROUND_INST: instantiating (5) with xp, all_122_0, xQ, simplifying with (1),
% 45.91/8.12 | (10) gives:
% 45.91/8.12 | (13) all_122_0 = xp
% 45.91/8.12 |
% 45.91/8.12 | COMBINE_EQS: (12), (13) imply:
% 45.91/8.12 | (14) all_94_0 = xp
% 45.91/8.12 |
% 45.91/8.12 | SIMP: (14) implies:
% 45.91/8.12 | (15) all_94_0 = xp
% 45.91/8.12 |
% 45.91/8.12 | REDUCE: (11), (15) imply:
% 45.91/8.12 | (16) $false
% 45.91/8.12 |
% 45.91/8.12 | CLOSE: (16) is inconsistent.
% 45.91/8.12 |
% 45.91/8.12 End of proof
% 45.91/8.12 % SZS output end Proof for theBenchmark
% 45.91/8.12
% 45.91/8.12 7542ms
%------------------------------------------------------------------------------