TSTP Solution File: NUM565+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM565+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 : n031.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 11:48:39 EDT 2023
% Result : Theorem 18.61s 3.29s
% Output : Proof 31.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM565+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:27:07 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.02/1.36 Prover 4: Preprocessing ...
% 4.02/1.36 Prover 1: Preprocessing ...
% 4.78/1.40 Prover 3: Preprocessing ...
% 4.78/1.40 Prover 6: Preprocessing ...
% 4.78/1.40 Prover 2: Preprocessing ...
% 4.78/1.40 Prover 0: Preprocessing ...
% 4.78/1.41 Prover 5: Preprocessing ...
% 13.31/2.54 Prover 1: Constructing countermodel ...
% 13.31/2.58 Prover 3: Constructing countermodel ...
% 13.31/2.63 Prover 6: Proving ...
% 14.45/2.75 Prover 5: Proving ...
% 18.61/3.29 Prover 3: proved (2638ms)
% 18.61/3.29
% 18.61/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.61/3.29
% 18.61/3.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.61/3.31 Prover 6: stopped
% 18.61/3.32 Prover 5: stopped
% 18.61/3.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.61/3.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.77/3.51 Prover 10: Preprocessing ...
% 20.77/3.52 Prover 8: Preprocessing ...
% 20.92/3.55 Prover 7: Preprocessing ...
% 20.92/3.58 Prover 2: Proving ...
% 20.92/3.61 Prover 2: stopped
% 21.64/3.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.13/3.82 Prover 11: Preprocessing ...
% 23.97/4.04 Prover 7: Constructing countermodel ...
% 25.92/4.19 Prover 8: Warning: ignoring some quantifiers
% 26.10/4.21 Prover 8: Constructing countermodel ...
% 26.89/4.35 Prover 10: Constructing countermodel ...
% 28.27/4.49 Prover 1: Found proof (size 34)
% 28.27/4.49 Prover 1: proved (3854ms)
% 28.27/4.49 Prover 11: stopped
% 28.27/4.49 Prover 10: stopped
% 28.27/4.49 Prover 8: stopped
% 28.27/4.49 Prover 7: stopped
% 29.46/4.78 Prover 4: Constructing countermodel ...
% 29.95/4.82 Prover 4: stopped
% 30.65/5.06 Prover 0: Proving ...
% 30.65/5.08 Prover 0: stopped
% 30.65/5.08
% 30.65/5.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.65/5.08
% 30.65/5.08 % SZS output start Proof for theBenchmark
% 31.07/5.09 Assumptions after simplification:
% 31.07/5.09 ---------------------------------
% 31.07/5.09
% 31.07/5.09 (mCardEmpty)
% 31.16/5.14 $i(sz00) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) |
% 31.16/5.14 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | (( ~ (v1 = sz00)
% 31.16/5.14 | v0 = slcrc0) & ( ~ (v0 = slcrc0) | v1 = sz00)))
% 31.16/5.14
% 31.16/5.14 (mCountNFin_01)
% 31.16/5.14 $i(slcrc0) & ( ~ (isCountable0(slcrc0) = 0) | ? [v0: int] : ( ~ (v0 = 0) &
% 31.16/5.14 aSet0(slcrc0) = v0))
% 31.16/5.14
% 31.16/5.14 (mDefSub)
% 31.16/5.15 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] :
% 31.16/5.15 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 31.16/5.15 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) =
% 31.16/5.15 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & !
% 31.16/5.15 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & !
% 31.16/5.15 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 31.16/5.15 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) =
% 31.16/5.15 v4))))))
% 31.16/5.15
% 31.16/5.15 (m__)
% 31.16/5.16 $i(xc) & $i(xS) & $i(sz00) & $i(slcrc0) & ? [v0: $i] : ? [v1: any] : ? [v2:
% 31.16/5.16 $i] : (sdtlpdtrp0(xc, slcrc0) = v2 & slbdtsldtrb0(xS, sz00) = v0 &
% 31.16/5.16 aSet0(slcrc0) = v1 & $i(v2) & $i(v0) & ? [v3: $i] : ? [v4: $i] : (v1 = 0 &
% 31.16/5.16 ~ (v4 = v2) & sdtlpdtrp0(xc, v3) = v4 & sbrdtbr0(v3) = sz00 &
% 31.16/5.16 aSubsetOf0(v3, xS) = 0 & aSet0(v3) = 0 & aElementOf0(v3, v0) = 0 & $i(v4)
% 31.16/5.16 & $i(v3) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (aElementOf0(v5, xS)
% 31.16/5.16 = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & aElementOf0(v5, v3)
% 31.16/5.16 = v7)) & ! [v5: $i] : ( ~ (aElementOf0(v5, slcrc0) = 0) | ~
% 31.16/5.16 $i(v5))))
% 31.16/5.16
% 31.16/5.16 (m__3435)
% 31.16/5.16 aSubsetOf0(xS, szNzAzT0) = 0 & isCountable0(xS) = 0 & aSet0(xS) = 0 & $i(xS) &
% 31.16/5.16 $i(szNzAzT0) & ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ $i(v0) |
% 31.16/5.16 aElementOf0(v0, szNzAzT0) = 0)
% 31.16/5.16
% 31.16/5.16 (function-axioms)
% 31.16/5.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.16/5.17 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.16/5.17 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 31.16/5.17 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 31.16/5.17 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 31.16/5.17 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 31.16/5.17 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 31.16/5.18 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 31.16/5.18 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 31.16/5.18 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.16/5.18 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 31.16/5.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 31.16/5.18 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 31.16/5.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.16/5.18 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.16/5.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 31.16/5.18 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.16/5.18 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.16/5.18 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 31.16/5.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 31.16/5.18 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 31.16/5.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 31.16/5.18 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.16/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 31.16/5.18 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 31.16/5.18 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 31.16/5.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 31.16/5.18 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.16/5.18 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 31.16/5.18 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 31.16/5.18 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.16/5.18 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 31.16/5.18 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 31.16/5.18 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 31.16/5.18 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 31.16/5.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 31.16/5.18 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 31.16/5.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 31.16/5.18 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 31.16/5.18 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 31.16/5.18 ~ (aElement0(v2) = v0))
% 31.16/5.18
% 31.16/5.18 Further assumptions not needed in the proof:
% 31.16/5.18 --------------------------------------------
% 31.16/5.18 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardNum, mCardS, mCardSeg,
% 31.16/5.18 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff,
% 31.16/5.18 mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 31.16/5.18 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 31.16/5.18 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 31.16/5.18 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 31.16/5.18 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 31.16/5.18 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 31.16/5.18 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 31.16/5.18 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3453, m__3462, m__3476
% 31.16/5.18
% 31.16/5.18 Those formulas are unsatisfiable:
% 31.16/5.18 ---------------------------------
% 31.16/5.18
% 31.16/5.18 Begin of proof
% 31.16/5.18 |
% 31.16/5.18 | ALPHA: (mCountNFin_01) implies:
% 31.16/5.18 | (1) ~ (isCountable0(slcrc0) = 0) | ? [v0: int] : ( ~ (v0 = 0) &
% 31.16/5.18 | aSet0(slcrc0) = v0)
% 31.16/5.18 |
% 31.16/5.18 | ALPHA: (mCardEmpty) implies:
% 31.16/5.18 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ?
% 31.16/5.18 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | (( ~ (v1 = sz00) | v0 =
% 31.16/5.18 | slcrc0) & ( ~ (v0 = slcrc0) | v1 = sz00)))
% 31.16/5.18 |
% 31.16/5.18 | ALPHA: (m__3435) implies:
% 31.16/5.18 | (3) aSet0(xS) = 0
% 31.16/5.18 |
% 31.16/5.18 | ALPHA: (m__) implies:
% 31.16/5.19 | (4) $i(xS)
% 31.16/5.19 | (5) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : (sdtlpdtrp0(xc, slcrc0) = v2
% 31.16/5.19 | & slbdtsldtrb0(xS, sz00) = v0 & aSet0(slcrc0) = v1 & $i(v2) & $i(v0)
% 31.16/5.19 | & ? [v3: $i] : ? [v4: $i] : (v1 = 0 & ~ (v4 = v2) & sdtlpdtrp0(xc,
% 31.16/5.19 | v3) = v4 & sbrdtbr0(v3) = sz00 & aSubsetOf0(v3, xS) = 0 &
% 31.16/5.19 | aSet0(v3) = 0 & aElementOf0(v3, v0) = 0 & $i(v4) & $i(v3) & ! [v5:
% 31.16/5.19 | $i] : ! [v6: int] : (v6 = 0 | ~ (aElementOf0(v5, xS) = v6) | ~
% 31.16/5.19 | $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & aElementOf0(v5, v3) = v7))
% 31.16/5.19 | & ! [v5: $i] : ( ~ (aElementOf0(v5, slcrc0) = 0) | ~ $i(v5))))
% 31.16/5.19 |
% 31.16/5.19 | ALPHA: (function-axioms) implies:
% 31.16/5.19 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 31.16/5.19 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 31.16/5.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.16/5.19 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 31.16/5.19 |
% 31.16/5.19 | DELTA: instantiating (5) with fresh symbols all_69_0, all_69_1, all_69_2
% 31.16/5.19 | gives:
% 31.16/5.19 | (8) sdtlpdtrp0(xc, slcrc0) = all_69_0 & slbdtsldtrb0(xS, sz00) = all_69_2 &
% 31.16/5.19 | aSet0(slcrc0) = all_69_1 & $i(all_69_0) & $i(all_69_2) & ? [v0: $i] :
% 31.16/5.19 | ? [v1: any] : (all_69_1 = 0 & ~ (v1 = all_69_0) & sdtlpdtrp0(xc, v0) =
% 31.16/5.19 | v1 & sbrdtbr0(v0) = sz00 & aSubsetOf0(v0, xS) = 0 & aSet0(v0) = 0 &
% 31.16/5.19 | aElementOf0(v0, all_69_2) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 31.16/5.20 | [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xS) = v3) | ~ $i(v2) | ?
% 31.16/5.20 | [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v0) = v4)) & ! [v2: $i]
% 31.16/5.20 | : ( ~ (aElementOf0(v2, slcrc0) = 0) | ~ $i(v2)))
% 31.16/5.20 |
% 31.16/5.20 | ALPHA: (8) implies:
% 31.16/5.20 | (9) aSet0(slcrc0) = all_69_1
% 31.16/5.20 | (10) sdtlpdtrp0(xc, slcrc0) = all_69_0
% 31.16/5.20 | (11) ? [v0: $i] : ? [v1: any] : (all_69_1 = 0 & ~ (v1 = all_69_0) &
% 31.16/5.20 | sdtlpdtrp0(xc, v0) = v1 & sbrdtbr0(v0) = sz00 & aSubsetOf0(v0, xS) =
% 31.16/5.20 | 0 & aSet0(v0) = 0 & aElementOf0(v0, all_69_2) = 0 & $i(v1) & $i(v0)
% 31.16/5.20 | & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xS) =
% 31.16/5.20 | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2,
% 31.16/5.20 | v0) = v4)) & ! [v2: $i] : ( ~ (aElementOf0(v2, slcrc0) = 0) |
% 31.16/5.20 | ~ $i(v2)))
% 31.16/5.20 |
% 31.16/5.20 | DELTA: instantiating (11) with fresh symbols all_74_0, all_74_1 gives:
% 31.16/5.20 | (12) all_69_1 = 0 & ~ (all_74_0 = all_69_0) & sdtlpdtrp0(xc, all_74_1) =
% 31.16/5.20 | all_74_0 & sbrdtbr0(all_74_1) = sz00 & aSubsetOf0(all_74_1, xS) = 0 &
% 31.16/5.20 | aSet0(all_74_1) = 0 & aElementOf0(all_74_1, all_69_2) = 0 &
% 31.16/5.20 | $i(all_74_0) & $i(all_74_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 31.16/5.20 | ~ (aElementOf0(v0, xS) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 31.16/5.20 | 0) & aElementOf0(v0, all_74_1) = v2)) & ! [v0: $i] : ( ~
% 31.16/5.20 | (aElementOf0(v0, slcrc0) = 0) | ~ $i(v0))
% 31.16/5.20 |
% 31.16/5.20 | ALPHA: (12) implies:
% 31.16/5.20 | (13) all_69_1 = 0
% 31.16/5.20 | (14) ~ (all_74_0 = all_69_0)
% 31.16/5.20 | (15) $i(all_74_1)
% 31.16/5.20 | (16) aSubsetOf0(all_74_1, xS) = 0
% 31.16/5.20 | (17) sbrdtbr0(all_74_1) = sz00
% 31.16/5.20 | (18) sdtlpdtrp0(xc, all_74_1) = all_74_0
% 31.16/5.20 |
% 31.16/5.20 | REDUCE: (9), (13) imply:
% 31.16/5.20 | (19) aSet0(slcrc0) = 0
% 31.16/5.20 |
% 31.16/5.20 | BETA: splitting (1) gives:
% 31.16/5.20 |
% 31.16/5.20 | Case 1:
% 31.16/5.20 | |
% 31.16/5.20 | |
% 31.16/5.20 | | GROUND_INST: instantiating (mDefSub) with xS, simplifying with (3), (4)
% 31.16/5.20 | | gives:
% 31.16/5.20 | | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xS) = v1)
% 31.16/5.20 | | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 31.16/5.20 | | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xS) = v3 & $i(v2)) |
% 31.16/5.20 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 31.16/5.20 | | (aSubsetOf0(v0, xS) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1:
% 31.16/5.20 | | $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xS) = v2) |
% 31.16/5.20 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0)
% 31.16/5.20 | | = v3))))
% 31.16/5.20 | |
% 31.16/5.20 | | ALPHA: (20) implies:
% 31.16/5.20 | | (21) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xS) = 0) | ~ $i(v0) | (aSet0(v0)
% 31.16/5.20 | | = 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1,
% 31.16/5.20 | | xS) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 31.16/5.20 | | aElementOf0(v1, v0) = v3))))
% 31.16/5.20 | |
% 31.62/5.21 | | GROUND_INST: instantiating (2) with all_74_1, sz00, simplifying with (15),
% 31.62/5.21 | | (17) gives:
% 31.62/5.21 | | (22) all_74_1 = slcrc0 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_74_1) =
% 31.62/5.21 | | v0)
% 31.62/5.21 | |
% 31.62/5.21 | | GROUND_INST: instantiating (21) with all_74_1, simplifying with (15), (16)
% 31.62/5.21 | | gives:
% 31.62/5.21 | | (23) aSet0(all_74_1) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 31.62/5.21 | | (aElementOf0(v0, xS) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 31.62/5.21 | | 0) & aElementOf0(v0, all_74_1) = v2))
% 31.62/5.21 | |
% 31.62/5.21 | | ALPHA: (23) implies:
% 31.62/5.21 | | (24) aSet0(all_74_1) = 0
% 31.62/5.21 | |
% 31.62/5.21 | | BETA: splitting (22) gives:
% 31.62/5.21 | |
% 31.62/5.21 | | Case 1:
% 31.62/5.21 | | |
% 31.62/5.21 | | | (25) all_74_1 = slcrc0
% 31.62/5.21 | | |
% 31.62/5.21 | | | REDUCE: (18), (25) imply:
% 31.62/5.21 | | | (26) sdtlpdtrp0(xc, slcrc0) = all_74_0
% 31.62/5.21 | | |
% 31.62/5.21 | | | GROUND_INST: instantiating (7) with all_69_0, all_74_0, slcrc0, xc,
% 31.62/5.21 | | | simplifying with (10), (26) gives:
% 31.62/5.21 | | | (27) all_74_0 = all_69_0
% 31.62/5.21 | | |
% 31.62/5.21 | | | REDUCE: (14), (27) imply:
% 31.62/5.21 | | | (28) $false
% 31.62/5.21 | | |
% 31.62/5.21 | | | CLOSE: (28) is inconsistent.
% 31.62/5.21 | | |
% 31.62/5.21 | | Case 2:
% 31.62/5.21 | | |
% 31.62/5.21 | | | (29) ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_74_1) = v0)
% 31.62/5.21 | | |
% 31.62/5.21 | | | DELTA: instantiating (29) with fresh symbol all_247_0 gives:
% 31.62/5.21 | | | (30) ~ (all_247_0 = 0) & aSet0(all_74_1) = all_247_0
% 31.62/5.21 | | |
% 31.62/5.21 | | | ALPHA: (30) implies:
% 31.62/5.21 | | | (31) ~ (all_247_0 = 0)
% 31.62/5.21 | | | (32) aSet0(all_74_1) = all_247_0
% 31.62/5.21 | | |
% 31.62/5.21 | | | GROUND_INST: instantiating (6) with 0, all_247_0, all_74_1, simplifying
% 31.62/5.21 | | | with (24), (32) gives:
% 31.62/5.21 | | | (33) all_247_0 = 0
% 31.62/5.21 | | |
% 31.62/5.21 | | | REDUCE: (31), (33) imply:
% 31.62/5.21 | | | (34) $false
% 31.62/5.21 | | |
% 31.62/5.21 | | | CLOSE: (34) is inconsistent.
% 31.62/5.21 | | |
% 31.62/5.21 | | End of split
% 31.62/5.21 | |
% 31.62/5.21 | Case 2:
% 31.62/5.21 | |
% 31.62/5.21 | | (35) ? [v0: int] : ( ~ (v0 = 0) & aSet0(slcrc0) = v0)
% 31.62/5.21 | |
% 31.62/5.21 | | DELTA: instantiating (35) with fresh symbol all_81_0 gives:
% 31.62/5.21 | | (36) ~ (all_81_0 = 0) & aSet0(slcrc0) = all_81_0
% 31.62/5.21 | |
% 31.62/5.21 | | ALPHA: (36) implies:
% 31.62/5.21 | | (37) ~ (all_81_0 = 0)
% 31.62/5.21 | | (38) aSet0(slcrc0) = all_81_0
% 31.62/5.21 | |
% 31.62/5.21 | | GROUND_INST: instantiating (6) with 0, all_81_0, slcrc0, simplifying with
% 31.62/5.21 | | (19), (38) gives:
% 31.62/5.21 | | (39) all_81_0 = 0
% 31.62/5.21 | |
% 31.62/5.21 | | REDUCE: (37), (39) imply:
% 31.62/5.21 | | (40) $false
% 31.62/5.21 | |
% 31.62/5.21 | | CLOSE: (40) is inconsistent.
% 31.62/5.21 | |
% 31.62/5.21 | End of split
% 31.62/5.21 |
% 31.62/5.21 End of proof
% 31.62/5.21 % SZS output end Proof for theBenchmark
% 31.62/5.21
% 31.62/5.21 4594ms
%------------------------------------------------------------------------------