%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM603+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 11:48:54 EDT 2023 % Result : Theorem 52.03s 7.87s % Output : Proof 68.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUM603+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.32 % Computer : n020.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Fri Aug 25 09:51:30 EDT 2023 % 0.10/0.32 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.63 Running up to 7 provers in parallel. % 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.05/1.61 Prover 1: Preprocessing ... % 5.05/1.62 Prover 4: Preprocessing ... % 6.00/1.65 Prover 3: Preprocessing ... % 6.00/1.65 Prover 0: Preprocessing ... % 6.00/1.65 Prover 2: Preprocessing ... % 6.00/1.66 Prover 6: Preprocessing ... % 6.00/1.66 Prover 5: Preprocessing ... % 19.09/3.44 Prover 1: Constructing countermodel ... % 19.09/3.45 Prover 3: Constructing countermodel ... % 19.09/3.46 Prover 6: Proving ... % 20.02/3.71 Prover 5: Proving ... % 24.61/4.21 Prover 2: Proving ... % 30.96/5.20 Prover 4: Constructing countermodel ... % 35.17/5.61 Prover 0: Proving ... % 52.03/7.85 Prover 3: proved (7210ms) % 52.03/7.87 % 52.03/7.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 52.03/7.87 % 52.03/7.87 Prover 6: stopped % 52.03/7.87 Prover 0: stopped % 52.48/7.87 Prover 2: stopped % 52.48/7.87 Prover 5: stopped % 52.48/7.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 52.48/7.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 52.48/7.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 52.48/7.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 52.48/7.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 53.71/8.08 Prover 8: Preprocessing ... % 54.28/8.12 Prover 11: Preprocessing ... % 54.81/8.30 Prover 7: Preprocessing ... % 54.81/8.32 Prover 13: Preprocessing ... % 54.81/8.33 Prover 10: Preprocessing ... % 57.43/8.54 Prover 8: Warning: ignoring some quantifiers % 57.43/8.56 Prover 8: Constructing countermodel ... % 58.40/8.71 Prover 7: Constructing countermodel ... % 59.80/8.98 Prover 10: Constructing countermodel ... % 62.10/9.25 Prover 13: Warning: ignoring some quantifiers % 62.88/9.27 Prover 13: Constructing countermodel ... % 65.70/9.69 Prover 10: Found proof (size 19) % 65.70/9.69 Prover 10: proved (1814ms) % 65.70/9.69 Prover 7: stopped % 65.70/9.69 Prover 1: stopped % 65.70/9.69 Prover 13: stopped % 65.70/9.69 Prover 8: stopped % 65.70/9.70 Prover 4: stopped % 67.67/10.08 Prover 11: Constructing countermodel ... % 67.67/10.13 Prover 11: stopped % 67.67/10.13 % 67.67/10.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 67.67/10.13 % 67.67/10.14 % SZS output start Proof for theBenchmark % 67.93/10.15 Assumptions after simplification: % 67.93/10.15 --------------------------------- % 67.93/10.15 % 67.93/10.15 (mZeroLess) % 67.93/10.16 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 67.93/10.16 szNzAzT0) | sdtlseqdt0(sz00, v0)) % 67.93/10.16 % 67.93/10.16 (mZeroNum) % 67.93/10.16 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 67.93/10.16 % 67.93/10.16 (m__) % 68.02/10.19 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & % 68.02/10.19 ~ aSubsetOf0(v0, xS)) % 68.02/10.19 % 68.02/10.19 (m__3623) % 68.02/10.19 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 68.02/10.19 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 68.02/10.19 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 68.02/10.19 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 68.02/10.19 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i] % 68.02/10.19 : (sdtlpdtrp0(xN, v4) = v5 & szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & % 68.02/10.19 aSubsetOf0(v5, v3) & isCountable0(v5))) % 68.02/10.20 % 68.02/10.20 (m__3754) % 68.02/10.20 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 68.02/10.20 : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) | % 68.02/10.20 ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 68.02/10.20 aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 68.02/10.20 % 68.02/10.20 (m__4660) % 68.02/10.20 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 68.02/10.20 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 68.02/10.20 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 68.02/10.20 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 68.02/10.20 % 68.02/10.20 (m__5034) % 68.02/10.20 sdtlpdtrp0(xe, xi) = xx & $i(xi) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 68.02/10.20 aElementOf0(xi, szNzAzT0) % 68.02/10.20 % 68.02/10.20 (function-axioms) % 68.02/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.02/10.21 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 68.02/10.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 68.02/10.21 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 68.02/10.21 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 68.02/10.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 68.02/10.21 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 68.02/10.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 68.02/10.21 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 68.02/10.21 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 68.02/10.21 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 68.02/10.21 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 68.02/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 68.02/10.21 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 68.02/10.21 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 68.02/10.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 68.02/10.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 68.02/10.21 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 68.02/10.21 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 68.02/10.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 68.02/10.21 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 68.02/10.21 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 68.02/10.21 v0)) % 68.02/10.21 % 68.02/10.21 Further assumptions not needed in the proof: % 68.02/10.21 -------------------------------------------- % 68.02/10.22 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 68.02/10.22 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 68.02/10.22 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 68.02/10.22 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 68.02/10.22 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 68.02/10.22 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 68.02/10.22 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 68.02/10.22 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 68.02/10.22 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 68.02/10.22 mSuccEquSucc, mSuccLess, mSuccNum, m__3291, m__3398, m__3418, m__3435, m__3453, % 68.02/10.22 m__3462, m__3520, m__3533, m__3671, m__3821, m__3965, m__4151, m__4182, m__4331, % 68.02/10.22 m__4411, m__4618, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__5009 % 68.02/10.22 % 68.02/10.22 Those formulas are unsatisfiable: % 68.02/10.22 --------------------------------- % 68.02/10.22 % 68.02/10.22 Begin of proof % 68.02/10.22 | % 68.02/10.22 | ALPHA: (mZeroNum) implies: % 68.28/10.22 | (1) aElementOf0(sz00, szNzAzT0) % 68.28/10.22 | % 68.28/10.22 | ALPHA: (mZeroLess) implies: % 68.28/10.22 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 68.28/10.22 | sdtlseqdt0(sz00, v0)) % 68.28/10.22 | % 68.28/10.22 | ALPHA: (m__3623) implies: % 68.28/10.22 | (3) $i(sz00) % 68.28/10.22 | (4) sdtlpdtrp0(xN, sz00) = xS % 68.28/10.22 | % 68.28/10.22 | ALPHA: (m__3754) implies: % 68.28/10.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 68.28/10.22 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) % 68.28/10.22 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | % 68.28/10.22 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 68.28/10.22 | % 68.28/10.22 | ALPHA: (m__4660) implies: % 68.28/10.22 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 68.28/10.22 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 68.28/10.22 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 68.28/10.22 | % 68.28/10.22 | ALPHA: (m__5034) implies: % 68.28/10.22 | (7) aElementOf0(xi, szNzAzT0) % 68.28/10.22 | (8) sdtlpdtrp0(xe, xi) = xx % 68.28/10.22 | % 68.28/10.22 | ALPHA: (m__) implies: % 68.28/10.23 | (9) $i(xi) % 68.28/10.23 | (10) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & ~ aSubsetOf0(v0, % 68.28/10.23 | xS)) % 68.28/10.23 | % 68.28/10.23 | ALPHA: (function-axioms) implies: % 68.28/10.23 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.28/10.23 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 68.28/10.23 | % 68.28/10.23 | DELTA: instantiating (10) with fresh symbol all_76_0 gives: % 68.28/10.23 | (12) sdtlpdtrp0(xN, xi) = all_76_0 & $i(all_76_0) & ~ aSubsetOf0(all_76_0, % 68.28/10.23 | xS) % 68.28/10.23 | % 68.28/10.23 | ALPHA: (12) implies: % 68.28/10.23 | (13) ~ aSubsetOf0(all_76_0, xS) % 68.28/10.23 | (14) sdtlpdtrp0(xN, xi) = all_76_0 % 68.28/10.23 | % 68.28/10.23 | GROUND_INST: instantiating (2) with xi, simplifying with (7), (9) gives: % 68.28/10.23 | (15) sdtlseqdt0(sz00, xi) % 68.28/10.23 | % 68.28/10.23 | GROUND_INST: instantiating (6) with xi, xx, simplifying with (7), (8), (9) % 68.28/10.23 | gives: % 68.28/10.23 | (16) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = xx & $i(v0) % 68.28/10.23 | & $i(xx)) % 68.28/10.23 | % 68.28/10.23 | DELTA: instantiating (16) with fresh symbol all_110_0 gives: % 68.28/10.23 | (17) sdtlpdtrp0(xN, xi) = all_110_0 & szmzizndt0(all_110_0) = xx & % 68.28/10.23 | $i(all_110_0) & $i(xx) % 68.28/10.23 | % 68.28/10.23 | ALPHA: (17) implies: % 68.28/10.23 | (18) sdtlpdtrp0(xN, xi) = all_110_0 % 68.28/10.23 | % 68.28/10.23 | GROUND_INST: instantiating (11) with all_76_0, all_110_0, xi, xN, simplifying % 68.28/10.23 | with (14), (18) gives: % 68.28/10.23 | (19) all_110_0 = all_76_0 % 68.28/10.23 | % 68.28/10.23 | GROUND_INST: instantiating (5) with xi, sz00, all_76_0, xS, simplifying with % 68.28/10.23 | (1), (3), (4), (7), (9), (13), (14), (15) gives: % 68.28/10.23 | (20) $false % 68.28/10.24 | % 68.28/10.24 | CLOSE: (20) is inconsistent. % 68.28/10.24 | % 68.28/10.24 End of proof % 68.28/10.24 % SZS output end Proof for theBenchmark % 68.28/10.24 % 68.28/10.24 9623ms %------------------------------------------------------------------------------