%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM568+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 : n010.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 20.45s 3.50s % Output : Proof 29.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM568+1 : TPTP v8.1.2. Released v4.0.0. % 0.15/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n010.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Aug 25 11:49:05 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.55/1.36 Prover 4: Preprocessing ... % 4.55/1.36 Prover 1: Preprocessing ... % 4.55/1.41 Prover 0: Preprocessing ... % 4.55/1.41 Prover 6: Preprocessing ... % 4.55/1.41 Prover 3: Preprocessing ... % 4.55/1.41 Prover 5: Preprocessing ... % 4.55/1.41 Prover 2: Preprocessing ... % 12.92/2.55 Prover 6: Proving ... % 12.92/2.55 Prover 1: Constructing countermodel ... % 12.92/2.56 Prover 3: Constructing countermodel ... % 12.92/2.59 Prover 5: Proving ... % 15.20/2.85 Prover 2: Proving ... % 18.35/3.24 Prover 0: Proving ... % 18.95/3.30 Prover 4: Constructing countermodel ... % 20.26/3.49 Prover 3: proved (2847ms) % 20.26/3.50 % 20.45/3.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.45/3.50 % 20.45/3.51 Prover 2: stopped % 20.45/3.51 Prover 6: stopped % 20.45/3.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.45/3.51 Prover 5: stopped % 20.45/3.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.45/3.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.45/3.52 Prover 0: stopped % 20.45/3.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.60/3.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.35/3.69 Prover 11: Preprocessing ... % 22.51/3.78 Prover 8: Preprocessing ... % 22.51/3.78 Prover 10: Preprocessing ... % 22.51/3.78 Prover 7: Preprocessing ... % 22.51/3.79 Prover 13: Preprocessing ... % 23.66/3.98 Prover 10: Constructing countermodel ... % 24.34/4.03 Prover 7: Constructing countermodel ... % 24.34/4.07 Prover 8: Warning: ignoring some quantifiers % 24.34/4.08 Prover 8: Constructing countermodel ... % 24.95/4.12 Prover 13: Warning: ignoring some quantifiers % 24.95/4.15 Prover 13: Constructing countermodel ... % 26.62/4.32 Prover 10: Found proof (size 13) % 26.62/4.32 Prover 10: proved (807ms) % 26.62/4.32 Prover 8: stopped % 26.62/4.32 Prover 1: stopped % 26.62/4.32 Prover 7: stopped % 26.62/4.33 Prover 4: stopped % 26.62/4.33 Prover 13: stopped % 28.62/4.84 Prover 11: Constructing countermodel ... % 28.89/4.88 Prover 11: stopped % 28.89/4.88 % 28.89/4.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 28.89/4.88 % 28.89/4.89 % SZS output start Proof for theBenchmark % 28.89/4.90 Assumptions after simplification: % 28.89/4.90 --------------------------------- % 28.89/4.90 % 28.89/4.90 (mNatExtra) % 28.89/4.94 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 28.89/4.94 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 28.89/4.94 aElementOf0(v1, szNzAzT0))) % 28.89/4.94 % 28.89/4.94 (m__) % 28.89/4.94 $i(xK) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0) % 28.89/4.94 | ~ aElementOf0(v0, szNzAzT0)) % 28.89/4.94 % 28.89/4.94 (m__3418) % 28.89/4.94 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 28.89/4.94 % 28.89/4.94 (m__3462) % 28.89/4.94 ~ (xK = sz00) & $i(xK) & $i(sz00) % 28.89/4.94 % 28.89/4.94 (m__3520) % 28.89/4.95 ~ (xK = sz00) & $i(xK) & $i(sz00) % 28.89/4.95 % 28.89/4.95 Further assumptions not needed in the proof: % 28.89/4.95 -------------------------------------------- % 28.89/4.95 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 28.89/4.95 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 28.89/4.95 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 28.89/4.95 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 28.89/4.95 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 28.89/4.95 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 28.89/4.95 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet, % 28.89/4.95 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, % 28.89/4.95 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, % 28.89/4.95 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3435, m__3453 % 28.89/4.95 % 28.89/4.95 Those formulas are unsatisfiable: % 28.89/4.95 --------------------------------- % 28.89/4.95 % 28.89/4.95 Begin of proof % 28.89/4.95 | % 28.89/4.95 | ALPHA: (mNatExtra) implies: % 28.89/4.95 | (1) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 28.89/4.95 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 28.89/4.95 | szNzAzT0))) % 28.89/4.95 | % 28.89/4.95 | ALPHA: (m__3418) implies: % 28.89/4.95 | (2) aElementOf0(xK, szNzAzT0) % 28.89/4.95 | % 28.89/4.95 | ALPHA: (m__3520) implies: % 28.89/4.96 | (3) ~ (xK = sz00) % 28.89/4.96 | % 28.89/4.96 | ALPHA: (m__) implies: % 28.89/4.96 | (4) $i(xK) % 28.89/4.96 | (5) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0) | ~ % 28.89/4.96 | aElementOf0(v0, szNzAzT0)) % 28.89/4.96 | % 28.89/4.96 | GROUND_INST: instantiating (1) with xK, simplifying with (2), (4) gives: % 29.25/4.96 | (6) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 29.25/4.96 | aElementOf0(v0, szNzAzT0)) % 29.25/4.96 | % 29.25/4.96 | BETA: splitting (6) gives: % 29.25/4.96 | % 29.25/4.96 | Case 1: % 29.25/4.96 | | % 29.25/4.96 | | (7) xK = sz00 % 29.25/4.96 | | % 29.25/4.96 | | REDUCE: (3), (7) imply: % 29.25/4.96 | | (8) $false % 29.25/4.96 | | % 29.25/4.96 | | CLOSE: (8) is inconsistent. % 29.25/4.96 | | % 29.25/4.96 | Case 2: % 29.25/4.96 | | % 29.25/4.97 | | (9) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & aElementOf0(v0, % 29.25/4.97 | | szNzAzT0)) % 29.25/4.97 | | % 29.25/4.97 | | DELTA: instantiating (9) with fresh symbol all_85_0 gives: % 29.25/4.97 | | (10) szszuzczcdt0(all_85_0) = xK & $i(all_85_0) & aElementOf0(all_85_0, % 29.25/4.97 | | szNzAzT0) % 29.25/4.97 | | % 29.25/4.97 | | ALPHA: (10) implies: % 29.25/4.97 | | (11) aElementOf0(all_85_0, szNzAzT0) % 29.25/4.97 | | (12) $i(all_85_0) % 29.25/4.97 | | (13) szszuzczcdt0(all_85_0) = xK % 29.25/4.97 | | % 29.25/4.97 | | GROUND_INST: instantiating (5) with all_85_0, simplifying with (11), (12), % 29.25/4.97 | | (13) gives: % 29.25/4.97 | | (14) $false % 29.25/4.97 | | % 29.25/4.97 | | CLOSE: (14) is inconsistent. % 29.25/4.97 | | % 29.25/4.97 | End of split % 29.25/4.97 | % 29.25/4.97 End of proof % 29.25/4.97 % SZS output end Proof for theBenchmark % 29.25/4.97 % 29.25/4.97 4345ms %------------------------------------------------------------------------------