%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM605+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 : n017.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 11:48:55 EDT 2023 % Result : Theorem 24.53s 4.12s % Output : Proof 42.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM605+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 07:13:55 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 6.53/1.63 Prover 1: Preprocessing ... % 6.53/1.63 Prover 4: Preprocessing ... % 6.53/1.66 Prover 2: Preprocessing ... % 6.53/1.66 Prover 3: Preprocessing ... % 6.53/1.66 Prover 5: Preprocessing ... % 6.53/1.66 Prover 6: Preprocessing ... % 6.53/1.67 Prover 0: Preprocessing ... % 20.03/3.47 Prover 1: Constructing countermodel ... % 20.03/3.48 Prover 6: Proving ... % 20.03/3.48 Prover 3: Constructing countermodel ... % 22.51/3.86 Prover 5: Proving ... % 24.53/4.12 Prover 3: proved (3496ms) % 24.53/4.12 % 24.53/4.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.53/4.12 % 24.53/4.13 Prover 6: stopped % 24.53/4.13 Prover 5: stopped % 25.26/4.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 25.26/4.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 25.26/4.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.35/4.44 Prover 7: Preprocessing ... % 27.35/4.44 Prover 8: Preprocessing ... % 27.35/4.52 Prover 10: Preprocessing ... % 31.55/5.06 Prover 8: Warning: ignoring some quantifiers % 31.55/5.11 Prover 8: Constructing countermodel ... % 34.36/5.34 Prover 10: Constructing countermodel ... % 34.98/5.45 Prover 1: Found proof (size 36) % 34.98/5.45 Prover 1: proved (4834ms) % 34.98/5.45 Prover 10: stopped % 35.29/5.46 Prover 8: stopped % 35.86/5.56 Prover 7: Constructing countermodel ... % 35.86/5.57 Prover 7: stopped % 40.54/6.33 Prover 4: Constructing countermodel ... % 40.54/6.34 Prover 0: Constructing countermodel ... % 40.54/6.34 Prover 0: stopped % 40.54/6.35 Prover 4: stopped % 41.73/6.63 Prover 2: Constructing countermodel ... % 41.73/6.63 Prover 2: stopped % 41.73/6.63 % 41.73/6.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 41.73/6.63 % 42.10/6.64 % SZS output start Proof for theBenchmark % 42.10/6.65 Assumptions after simplification: % 42.10/6.65 --------------------------------- % 42.10/6.65 % 42.10/6.65 (mCardEmpty) % 42.35/6.71 $i(sz00) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | % 42.35/6.71 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | (( ~ (v1 = sz00) % 42.35/6.71 | v0 = slcrc0) & ( ~ (v0 = slcrc0) | v1 = sz00))) % 42.35/6.71 % 42.35/6.71 (mCountNFin_01) % 42.35/6.71 $i(slcrc0) & ( ~ (isCountable0(slcrc0) = 0) | ? [v0: int] : ( ~ (v0 = 0) & % 42.35/6.71 aSet0(slcrc0) = v0)) % 42.35/6.71 % 42.35/6.71 (mDefSub) % 42.35/6.72 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] : % 42.35/6.72 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 42.35/6.72 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) = % 42.35/6.72 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & ! % 42.35/6.72 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & ! % 42.35/6.72 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ % 42.35/6.72 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) = % 42.35/6.72 v4)))))) % 42.35/6.72 % 42.35/6.72 (m__) % 42.35/6.72 xQ = slcrc0 & $i(slcrc0) & ! [v0: $i] : ( ~ (aElementOf0(v0, slcrc0) = 0) | % 42.35/6.72 ~ $i(v0)) % 42.35/6.72 % 42.35/6.72 (m__3462) % 42.35/6.72 ~ (xK = sz00) & $i(xK) & $i(sz00) % 42.35/6.72 % 42.35/6.72 (m__3520) % 42.35/6.72 ~ (xK = sz00) & $i(xK) & $i(sz00) % 42.35/6.72 % 42.35/6.72 (m__4891) % 42.35/6.73 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 42.35/6.73 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 42.35/6.73 szDzozmdt0(xd) = v2 & aSet0(v1) = 0 & aSet0(xO) = 0 & $i(v2) & $i(v1) & % 42.35/6.73 $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = % 42.35/6.73 v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6 % 42.35/6.73 & aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 = 0)))) & % 42.35/6.73 ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, xO) = v4) | ~ % 42.35/6.73 $i(v3) | ! [v5: $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ $i(v5) | ? [v6: % 42.35/6.73 $i] : ( ~ (v6 = v3) & sdtlpdtrp0(xe, v5) = v6 & $i(v6)))) & ! [v3: % 42.35/6.73 $i] : ( ~ (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0 % 42.35/6.73 & aElementOf0(v3, v2) = 0)) & ! [v3: $i] : ( ~ (aElementOf0(v3, xO) = % 42.35/6.73 0) | ~ $i(v3) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 42.35/6.73 aElementOf0(v4, v1) = 0 & $i(v4)))) % 42.35/6.73 % 42.35/6.73 (m__5078) % 42.35/6.74 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 42.35/6.74 sbrdtbr0(xQ) = xK & aSubsetOf0(xQ, xO) = 0 & aSet0(xQ) = 0 & aElementOf0(xQ, % 42.35/6.74 v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ (aElementOf0(v1, xQ) = 0) | ~ $i(v1) % 42.35/6.74 | aElementOf0(v1, xO) = 0)) % 42.35/6.74 % 42.35/6.74 (function-axioms) % 42.35/6.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 42.35/6.75 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 42.35/6.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 42.35/6.75 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 42.35/6.75 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 42.35/6.75 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 42.35/6.75 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 42.35/6.75 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 42.35/6.75 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 42.35/6.75 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 42.35/6.75 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 42.35/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 42.35/6.75 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 42.35/6.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 42.35/6.75 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 42.35/6.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 42.35/6.75 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 42.35/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 42.35/6.75 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 42.35/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 42.35/6.75 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 42.35/6.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 42.35/6.75 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 42.35/6.75 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 42.35/6.75 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 42.35/6.75 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 42.35/6.75 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 42.35/6.75 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 42.35/6.75 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 42.35/6.75 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 42.35/6.75 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 42.35/6.75 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 42.35/6.75 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 42.35/6.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 42.35/6.75 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 42.35/6.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 42.35/6.75 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 42.35/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 42.35/6.75 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 42.35/6.75 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 42.35/6.75 ~ (aElement0(v2) = v0)) % 42.35/6.75 % 42.35/6.75 Further assumptions not needed in the proof: % 42.35/6.75 -------------------------------------------- % 42.35/6.75 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardNum, mCardS, mCardSeg, % 42.35/6.75 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, % 42.35/6.75 mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 42.35/6.75 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 42.35/6.75 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 42.35/6.75 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 42.35/6.75 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 42.35/6.75 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 42.35/6.75 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 42.35/6.75 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3533, % 42.35/6.75 m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, % 42.35/6.75 m__4618, m__4660, m__4730, m__4758, m__4854, m__4908, m__4982, m__4998 % 42.35/6.75 % 42.35/6.75 Those formulas are unsatisfiable: % 42.35/6.75 --------------------------------- % 42.35/6.75 % 42.35/6.75 Begin of proof % 42.66/6.75 | % 42.66/6.75 | ALPHA: (mCountNFin_01) implies: % 42.66/6.76 | (1) ~ (isCountable0(slcrc0) = 0) | ? [v0: int] : ( ~ (v0 = 0) & % 42.66/6.76 | aSet0(slcrc0) = v0) % 42.66/6.76 | % 42.66/6.76 | ALPHA: (mCardEmpty) implies: % 42.66/6.76 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ? % 42.66/6.76 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | (( ~ (v1 = sz00) | v0 = % 42.66/6.76 | slcrc0) & ( ~ (v0 = slcrc0) | v1 = sz00))) % 42.66/6.76 | % 42.66/6.76 | ALPHA: (m__3520) implies: % 42.66/6.76 | (3) ~ (xK = sz00) % 42.66/6.76 | % 42.66/6.76 | ALPHA: (m__4891) implies: % 42.66/6.76 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 42.66/6.76 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 42.66/6.76 | v2 & aSet0(v1) = 0 & aSet0(xO) = 0 & $i(v2) & $i(v1) & $i(v0) & ! % 42.66/6.76 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | % 42.66/6.76 | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6 & % 42.66/6.76 | aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 = % 42.66/6.76 | 0)))) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 42.66/6.76 | (aElementOf0(v3, xO) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~ % 42.66/6.76 | (aElementOf0(v5, v1) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = % 42.66/6.76 | v3) & sdtlpdtrp0(xe, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~ % 42.66/6.76 | (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0 & % 42.66/6.76 | aElementOf0(v3, v2) = 0)) & ! [v3: $i] : ( ~ (aElementOf0(v3, % 42.66/6.76 | xO) = 0) | ~ $i(v3) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 42.66/6.76 | aElementOf0(v4, v1) = 0 & $i(v4)))) % 42.66/6.76 | % 42.66/6.76 | ALPHA: (m__5078) implies: % 42.66/6.76 | (5) $i(xO) % 42.66/6.76 | (6) $i(xQ) % 42.66/6.76 | (7) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & % 42.71/6.76 | aSubsetOf0(xQ, xO) = 0 & aSet0(xQ) = 0 & aElementOf0(xQ, v0) = 0 & % 42.71/6.76 | $i(v0) & ! [v1: $i] : ( ~ (aElementOf0(v1, xQ) = 0) | ~ $i(v1) | % 42.71/6.76 | aElementOf0(v1, xO) = 0)) % 42.71/6.76 | % 42.71/6.76 | ALPHA: (m__) implies: % 42.71/6.76 | (8) xQ = slcrc0 % 42.71/6.76 | % 42.71/6.76 | ALPHA: (function-axioms) implies: % 42.71/6.76 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 42.71/6.76 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 42.71/6.76 | % 42.71/6.77 | DELTA: instantiating (7) with fresh symbol all_79_0 gives: % 42.71/6.77 | (10) slbdtsldtrb0(xO, xK) = all_79_0 & sbrdtbr0(xQ) = xK & aSubsetOf0(xQ, % 42.71/6.77 | xO) = 0 & aSet0(xQ) = 0 & aElementOf0(xQ, all_79_0) = 0 & % 42.71/6.77 | $i(all_79_0) & ! [v0: $i] : ( ~ (aElementOf0(v0, xQ) = 0) | ~ $i(v0) % 42.71/6.77 | | aElementOf0(v0, xO) = 0) % 42.71/6.77 | % 42.71/6.77 | ALPHA: (10) implies: % 42.71/6.77 | (11) aSet0(xQ) = 0 % 42.71/6.77 | (12) aSubsetOf0(xQ, xO) = 0 % 42.71/6.77 | (13) sbrdtbr0(xQ) = xK % 42.71/6.77 | % 42.71/6.77 | DELTA: instantiating (4) with fresh symbols all_91_0, all_91_1, all_91_2 % 42.71/6.77 | gives: % 42.71/6.77 | (14) szDzizrdt0(xd) = all_91_2 & sdtlcdtrc0(xe, all_91_1) = xO & % 42.71/6.77 | sdtlbdtrb0(xd, all_91_2) = all_91_1 & szDzozmdt0(xd) = all_91_0 & % 42.71/6.77 | aSet0(all_91_1) = 0 & aSet0(xO) = 0 & $i(all_91_0) & $i(all_91_1) & % 42.71/6.77 | $i(all_91_2) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 42.71/6.77 | (aElementOf0(v0, all_91_1) = v1) | ~ $i(v0) | ? [v2: any] : ? % 42.71/6.77 | [v3: $i] : (sdtlpdtrp0(xd, v0) = v3 & aElementOf0(v0, all_91_0) = v2 % 42.71/6.77 | & $i(v3) & ( ~ (v3 = all_91_2) | ~ (v2 = 0)))) & ! [v0: $i] : ! % 42.71/6.77 | [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xO) = v1) | ~ $i(v0) | ! % 42.71/6.77 | [v2: $i] : ( ~ (aElementOf0(v2, all_91_1) = 0) | ~ $i(v2) | ? [v3: % 42.71/6.77 | $i] : ( ~ (v3 = v0) & sdtlpdtrp0(xe, v2) = v3 & $i(v3)))) & ! % 42.71/6.77 | [v0: $i] : ( ~ (aElementOf0(v0, all_91_1) = 0) | ~ $i(v0) | % 42.71/6.77 | (sdtlpdtrp0(xd, v0) = all_91_2 & aElementOf0(v0, all_91_0) = 0)) & % 42.71/6.77 | ! [v0: $i] : ( ~ (aElementOf0(v0, xO) = 0) | ~ $i(v0) | ? [v1: $i] : % 42.71/6.77 | (sdtlpdtrp0(xe, v1) = v0 & aElementOf0(v1, all_91_1) = 0 & $i(v1))) % 42.71/6.77 | % 42.71/6.77 | ALPHA: (14) implies: % 42.71/6.77 | (15) aSet0(xO) = 0 % 42.71/6.77 | % 42.71/6.77 | REDUCE: (8), (13) imply: % 42.71/6.77 | (16) sbrdtbr0(slcrc0) = xK % 42.71/6.77 | % 42.71/6.77 | REDUCE: (8), (12) imply: % 42.71/6.77 | (17) aSubsetOf0(slcrc0, xO) = 0 % 42.71/6.77 | % 42.71/6.77 | REDUCE: (8), (11) imply: % 42.71/6.77 | (18) aSet0(slcrc0) = 0 % 42.71/6.77 | % 42.71/6.77 | REDUCE: (6), (8) imply: % 42.71/6.77 | (19) $i(slcrc0) % 42.71/6.77 | % 42.71/6.77 | BETA: splitting (1) gives: % 42.71/6.77 | % 42.71/6.77 | Case 1: % 42.71/6.77 | | % 42.71/6.77 | | % 42.71/6.77 | | GROUND_INST: instantiating (mDefSub) with xO, simplifying with (5), (15) % 42.71/6.77 | | gives: % 42.71/6.78 | | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xO) = v1) % 42.71/6.78 | | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 42.71/6.78 | | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xO) = v3 & $i(v2)) | % 42.71/6.78 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 42.71/6.78 | | (aSubsetOf0(v0, xO) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: % 42.71/6.78 | | $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xO) = v2) | % 42.71/6.78 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) % 42.71/6.78 | | = v3)))) % 42.71/6.78 | | % 42.71/6.78 | | ALPHA: (20) implies: % 42.71/6.78 | | (21) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xO) = 0) | ~ $i(v0) | (aSet0(v0) % 42.71/6.78 | | = 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 42.71/6.78 | | xO) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 42.71/6.78 | | aElementOf0(v1, v0) = v3)))) % 42.71/6.78 | | % 42.71/6.78 | | GROUND_INST: instantiating (2) with slcrc0, xK, simplifying with (16), (19) % 42.71/6.78 | | gives: % 42.71/6.78 | | (22) xK = sz00 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(slcrc0) = v0) % 42.71/6.78 | | % 42.71/6.78 | | GROUND_INST: instantiating (21) with slcrc0, simplifying with (17), (19) % 42.71/6.78 | | gives: % 42.71/6.78 | | (23) aSet0(slcrc0) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 42.71/6.78 | | (aElementOf0(v0, xO) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 42.71/6.78 | | 0) & aElementOf0(v0, slcrc0) = v2)) % 42.71/6.78 | | % 42.71/6.78 | | BETA: splitting (22) gives: % 42.71/6.78 | | % 42.71/6.78 | | Case 1: % 42.71/6.78 | | | % 42.71/6.78 | | | (24) xK = sz00 % 42.71/6.78 | | | % 42.71/6.78 | | | REDUCE: (3), (24) imply: % 42.71/6.78 | | | (25) $false % 42.71/6.78 | | | % 42.71/6.78 | | | CLOSE: (25) is inconsistent. % 42.71/6.78 | | | % 42.71/6.78 | | Case 2: % 42.71/6.78 | | | % 42.71/6.78 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & aSet0(slcrc0) = v0) % 42.71/6.78 | | | % 42.71/6.78 | | | DELTA: instantiating (26) with fresh symbol all_104_0 gives: % 42.71/6.78 | | | (27) ~ (all_104_0 = 0) & aSet0(slcrc0) = all_104_0 % 42.71/6.78 | | | % 42.71/6.78 | | | REF_CLOSE: (9), (18), (27) are inconsistent by sub-proof #1. % 42.71/6.78 | | | % 42.71/6.78 | | End of split % 42.71/6.78 | | % 42.71/6.78 | Case 2: % 42.71/6.78 | | % 42.71/6.78 | | (28) ? [v0: int] : ( ~ (v0 = 0) & aSet0(slcrc0) = v0) % 42.71/6.78 | | % 42.71/6.78 | | DELTA: instantiating (28) with fresh symbol all_104_0 gives: % 42.71/6.78 | | (29) ~ (all_104_0 = 0) & aSet0(slcrc0) = all_104_0 % 42.71/6.78 | | % 42.71/6.78 | | REF_CLOSE: (9), (18), (29) are inconsistent by sub-proof #1. % 42.71/6.78 | | % 42.71/6.78 | End of split % 42.71/6.78 | % 42.71/6.78 End of proof % 42.71/6.78 % 42.71/6.78 Sub-proof #1 shows that the following formulas are inconsistent: % 42.71/6.78 ---------------------------------------------------------------- % 42.71/6.78 (1) ~ (all_104_0 = 0) & aSet0(slcrc0) = all_104_0 % 42.71/6.78 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 42.71/6.78 (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 42.71/6.78 (3) aSet0(slcrc0) = 0 % 42.71/6.78 % 42.71/6.78 Begin of proof % 42.71/6.78 | % 42.71/6.78 | ALPHA: (1) implies: % 42.71/6.78 | (4) ~ (all_104_0 = 0) % 42.71/6.78 | (5) aSet0(slcrc0) = all_104_0 % 42.71/6.78 | % 42.71/6.78 | GROUND_INST: instantiating (2) with 0, all_104_0, slcrc0, simplifying with % 42.71/6.78 | (3), (5) gives: % 42.71/6.78 | (6) all_104_0 = 0 % 42.71/6.78 | % 42.71/6.78 | REDUCE: (4), (6) imply: % 42.71/6.78 | (7) $false % 42.71/6.78 | % 42.71/6.78 | CLOSE: (7) is inconsistent. % 42.71/6.78 | % 42.71/6.78 End of proof % 42.71/6.78 % SZS output end Proof for theBenchmark % 42.71/6.79 % 42.71/6.79 6183ms %------------------------------------------------------------------------------