%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM568+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 : n024.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 11:48:40 EDT 2023 % Result : Theorem 20.61s 3.52s % Output : Proof 31.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM568+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 15:26:39 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.23/1.33 Prover 4: Preprocessing ... % 4.23/1.33 Prover 1: Preprocessing ... % 4.94/1.36 Prover 6: Preprocessing ... % 4.94/1.36 Prover 0: Preprocessing ... % 4.94/1.36 Prover 3: Preprocessing ... % 4.94/1.36 Prover 2: Preprocessing ... % 4.94/1.36 Prover 5: Preprocessing ... % 13.67/2.48 Prover 1: Constructing countermodel ... % 14.24/2.55 Prover 6: Proving ... % 14.24/2.56 Prover 3: Constructing countermodel ... % 15.04/2.66 Prover 5: Proving ... % 18.25/3.11 Prover 2: Proving ... % 20.61/3.51 Prover 3: proved (2881ms) % 20.61/3.51 % 20.61/3.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.61/3.52 % 20.61/3.52 Prover 2: stopped % 20.61/3.52 Prover 6: stopped % 21.42/3.52 Prover 5: stopped % 21.42/3.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.42/3.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.42/3.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.42/3.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.75/3.70 Prover 7: Preprocessing ... % 22.75/3.72 Prover 10: Preprocessing ... % 22.75/3.73 Prover 11: Preprocessing ... % 22.75/3.73 Prover 8: Preprocessing ... % 23.75/3.82 Prover 4: Constructing countermodel ... % 25.08/4.04 Prover 7: Constructing countermodel ... % 25.78/4.05 Prover 8: Warning: ignoring some quantifiers % 25.78/4.05 Prover 0: Proving ... % 25.78/4.06 Prover 0: stopped % 25.78/4.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 25.78/4.06 Prover 10: Constructing countermodel ... % 25.78/4.07 Prover 8: Constructing countermodel ... % 26.32/4.15 Prover 13: Preprocessing ... % 27.77/4.34 Prover 10: Found proof (size 18) % 27.77/4.34 Prover 10: proved (817ms) % 27.77/4.34 Prover 7: stopped % 27.77/4.34 Prover 1: stopped % 27.77/4.34 Prover 8: stopped % 27.77/4.35 Prover 4: stopped % 28.76/4.49 Prover 13: Warning: ignoring some quantifiers % 28.76/4.51 Prover 13: Constructing countermodel ... % 28.76/4.53 Prover 13: stopped % 30.89/4.98 Prover 11: Constructing countermodel ... % 30.94/5.00 Prover 11: stopped % 30.94/5.00 % 30.94/5.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 30.94/5.00 % 30.94/5.00 % SZS output start Proof for theBenchmark % 31.03/5.01 Assumptions after simplification: % 31.03/5.01 --------------------------------- % 31.03/5.01 % 31.03/5.01 (mCountNFin_01) % 31.07/5.02 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 31.07/5.02 % 31.07/5.02 (mDefEmp) % 31.07/5.02 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 31.07/5.02 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 31.07/5.02 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 31.07/5.03 % 31.07/5.03 (mNatExtra) % 31.07/5.06 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 31.07/5.06 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 31.07/5.06 aElementOf0(v1, szNzAzT0))) % 31.07/5.06 % 31.07/5.06 (m__) % 31.07/5.06 $i(xK) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0) % 31.07/5.06 | ~ aElementOf0(v0, szNzAzT0)) % 31.07/5.06 % 31.07/5.06 (m__3418) % 31.07/5.06 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 31.07/5.06 % 31.07/5.06 (m__3462) % 31.07/5.06 ~ (xK = sz00) & $i(xK) & $i(sz00) % 31.07/5.06 % 31.07/5.06 (m__3520) % 31.07/5.06 ~ (xK = sz00) & $i(xK) & $i(sz00) % 31.07/5.06 % 31.07/5.06 Further assumptions not needed in the proof: % 31.07/5.06 -------------------------------------------- % 31.07/5.06 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 31.07/5.07 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 31.07/5.07 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 31.07/5.07 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 31.07/5.07 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 31.07/5.07 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 31.07/5.07 mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, % 31.07/5.07 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 31.07/5.07 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 31.07/5.07 mZeroNum, m__3291, m__3398, m__3435, m__3453 % 31.07/5.07 % 31.07/5.07 Those formulas are unsatisfiable: % 31.07/5.07 --------------------------------- % 31.07/5.07 % 31.07/5.07 Begin of proof % 31.07/5.07 | % 31.07/5.07 | ALPHA: (mDefEmp) implies: % 31.07/5.07 | (1) aSet0(slcrc0) % 31.07/5.07 | % 31.07/5.07 | ALPHA: (mCountNFin_01) implies: % 31.07/5.07 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 31.07/5.07 | % 31.07/5.07 | ALPHA: (mNatExtra) implies: % 31.07/5.07 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 31.07/5.07 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 31.07/5.07 | szNzAzT0))) % 31.07/5.07 | % 31.07/5.07 | ALPHA: (m__3418) implies: % 31.07/5.07 | (4) aElementOf0(xK, szNzAzT0) % 31.07/5.07 | % 31.07/5.07 | ALPHA: (m__3520) implies: % 31.07/5.07 | (5) ~ (xK = sz00) % 31.07/5.07 | % 31.07/5.07 | ALPHA: (m__) implies: % 31.07/5.07 | (6) $i(xK) % 31.07/5.07 | (7) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0) | ~ % 31.07/5.07 | aElementOf0(v0, szNzAzT0)) % 31.07/5.07 | % 31.07/5.07 | BETA: splitting (2) gives: % 31.07/5.07 | % 31.07/5.07 | Case 1: % 31.07/5.07 | | % 31.07/5.08 | | (8) ~ aSet0(slcrc0) % 31.07/5.08 | | % 31.07/5.08 | | PRED_UNIFY: (1), (8) imply: % 31.07/5.08 | | (9) $false % 31.07/5.08 | | % 31.07/5.08 | | CLOSE: (9) is inconsistent. % 31.07/5.08 | | % 31.07/5.08 | Case 2: % 31.07/5.08 | | % 31.07/5.08 | | % 31.07/5.08 | | GROUND_INST: instantiating (3) with xK, simplifying with (4), (6) gives: % 31.07/5.08 | | (10) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 31.07/5.08 | | aElementOf0(v0, szNzAzT0)) % 31.07/5.08 | | % 31.07/5.08 | | BETA: splitting (10) gives: % 31.07/5.08 | | % 31.07/5.08 | | Case 1: % 31.07/5.08 | | | % 31.07/5.08 | | | (11) xK = sz00 % 31.07/5.08 | | | % 31.07/5.08 | | | REDUCE: (5), (11) imply: % 31.07/5.08 | | | (12) $false % 31.07/5.08 | | | % 31.07/5.08 | | | CLOSE: (12) is inconsistent. % 31.07/5.08 | | | % 31.07/5.08 | | Case 2: % 31.07/5.08 | | | % 31.07/5.08 | | | (13) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & aElementOf0(v0, % 31.07/5.08 | | | szNzAzT0)) % 31.07/5.08 | | | % 31.07/5.08 | | | DELTA: instantiating (13) with fresh symbol all_91_0 gives: % 31.07/5.08 | | | (14) szszuzczcdt0(all_91_0) = xK & $i(all_91_0) & aElementOf0(all_91_0, % 31.07/5.08 | | | szNzAzT0) % 31.07/5.08 | | | % 31.07/5.08 | | | ALPHA: (14) implies: % 31.07/5.08 | | | (15) aElementOf0(all_91_0, szNzAzT0) % 31.07/5.08 | | | (16) $i(all_91_0) % 31.07/5.08 | | | (17) szszuzczcdt0(all_91_0) = xK % 31.07/5.08 | | | % 31.07/5.08 | | | GROUND_INST: instantiating (7) with all_91_0, simplifying with (15), (16), % 31.07/5.08 | | | (17) gives: % 31.07/5.08 | | | (18) $false % 31.07/5.08 | | | % 31.07/5.08 | | | CLOSE: (18) is inconsistent. % 31.07/5.08 | | | % 31.07/5.08 | | End of split % 31.07/5.08 | | % 31.07/5.08 | End of split % 31.07/5.08 | % 31.07/5.08 End of proof % 31.07/5.09 % SZS output end Proof for theBenchmark % 31.07/5.09 % 31.07/5.09 4476ms %------------------------------------------------------------------------------