%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM559+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 : n018.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 11:48:36 EDT 2023 % Result : Theorem 8.89s 1.93s % Output : Proof 13.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM559+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n018.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 16:04:44 EDT 2023 % 0.12/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.55/1.21 Prover 1: Preprocessing ... % 3.55/1.21 Prover 4: Preprocessing ... % 3.55/1.25 Prover 2: Preprocessing ... % 3.55/1.25 Prover 3: Preprocessing ... % 3.55/1.25 Prover 0: Preprocessing ... % 3.55/1.26 Prover 5: Preprocessing ... % 3.55/1.26 Prover 6: Preprocessing ... % 8.76/1.89 Prover 3: Constructing countermodel ... % 8.76/1.89 Prover 5: Constructing countermodel ... % 8.81/1.90 Prover 6: Constructing countermodel ... % 8.89/1.92 Prover 2: Constructing countermodel ... % 8.89/1.93 Prover 6: proved (1284ms) % 8.89/1.93 Prover 2: proved (1295ms) % 8.89/1.93 % 8.89/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.89/1.93 % 8.89/1.93 % 8.89/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.89/1.93 % 8.89/1.94 Prover 3: proved (1286ms) % 8.89/1.94 % 8.89/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.89/1.94 % 8.89/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.89/1.94 Prover 5: proved (1285ms) % 8.89/1.94 % 8.89/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.89/1.94 % 8.89/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.89/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.89/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.58/2.07 Prover 7: Preprocessing ... % 10.22/2.10 Prover 10: Preprocessing ... % 10.22/2.11 Prover 8: Preprocessing ... % 10.22/2.12 Prover 11: Preprocessing ... % 10.22/2.14 Prover 1: Constructing countermodel ... % 10.22/2.15 Prover 0: Constructing countermodel ... % 10.22/2.15 Prover 0: stopped % 10.22/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.98/2.30 Prover 13: Preprocessing ... % 12.23/2.40 Prover 1: Found proof (size 8) % 12.23/2.40 Prover 1: proved (1770ms) % 12.23/2.40 Prover 11: stopped % 12.47/2.43 Prover 10: Constructing countermodel ... % 12.63/2.43 Prover 13: stopped % 12.63/2.43 Prover 7: Constructing countermodel ... % 12.63/2.45 Prover 10: stopped % 12.63/2.45 Prover 7: stopped % 12.63/2.48 Prover 8: Warning: ignoring some quantifiers % 12.63/2.49 Prover 8: Constructing countermodel ... % 12.63/2.50 Prover 8: stopped % 12.63/2.52 Prover 4: Constructing countermodel ... % 13.23/2.54 Prover 4: stopped % 13.23/2.54 % 13.23/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.23/2.54 % 13.23/2.54 % SZS output start Proof for theBenchmark % 13.23/2.55 Assumptions after simplification: % 13.23/2.55 --------------------------------- % 13.23/2.55 % 13.23/2.55 (m__2323) % 13.23/2.57 $i(xQ) & $i(xx) & ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xQ) = v0) % 13.23/2.57 % 13.23/2.57 (m__2338) % 13.23/2.57 aElementOf0(xx, xQ) = 0 & $i(xQ) & $i(xx) % 13.23/2.57 % 13.23/2.57 (function-axioms) % 13.23/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.23/2.58 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: % 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.23/2.58 : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.23/2.58 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 13.23/2.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.23/2.58 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 13.23/2.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 13.23/2.58 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.23/2.58 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.23/2.58 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.23/2.58 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 13.23/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | % 13.23/2.58 ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 13.23/2.58 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! % 13.23/2.58 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ % 13.23/2.58 (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 13.23/2.58 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: % 13.23/2.58 $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 13.23/2.58 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | % 13.23/2.58 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 13.23/2.58 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 13.23/2.58 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 13.23/2.58 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 13.23/2.58 % 13.23/2.58 Further assumptions not needed in the proof: % 13.23/2.58 -------------------------------------------- % 13.23/2.58 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 13.23/2.58 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 13.23/2.58 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub, % 13.23/2.58 mDiffCons, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, % 13.23/2.58 mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 13.23/2.58 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 13.23/2.58 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, % 13.23/2.58 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 13.23/2.58 mZeroLess, mZeroNum, m__, m__2202, m__2202_02, m__2227, m__2256, m__2270, % 13.23/2.58 m__2291, m__2304 % 13.23/2.58 % 13.23/2.58 Those formulas are unsatisfiable: % 13.23/2.58 --------------------------------- % 13.23/2.58 % 13.23/2.58 Begin of proof % 13.23/2.58 | % 13.23/2.58 | ALPHA: (m__2323) implies: % 13.23/2.58 | (1) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xQ) = v0) % 13.23/2.58 | % 13.23/2.58 | ALPHA: (m__2338) implies: % 13.23/2.58 | (2) aElementOf0(xx, xQ) = 0 % 13.23/2.58 | % 13.23/2.58 | ALPHA: (function-axioms) implies: % 13.23/2.58 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.23/2.58 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 13.23/2.58 | (aElementOf0(v3, v2) = v0)) % 13.23/2.58 | % 13.23/2.58 | DELTA: instantiating (1) with fresh symbol all_55_0 gives: % 13.23/2.59 | (4) ~ (all_55_0 = 0) & aElementOf0(xx, xQ) = all_55_0 % 13.23/2.59 | % 13.23/2.59 | ALPHA: (4) implies: % 13.23/2.59 | (5) ~ (all_55_0 = 0) % 13.23/2.59 | (6) aElementOf0(xx, xQ) = all_55_0 % 13.23/2.59 | % 13.23/2.59 | GROUND_INST: instantiating (3) with 0, all_55_0, xQ, xx, simplifying with (2), % 13.23/2.59 | (6) gives: % 13.23/2.59 | (7) all_55_0 = 0 % 13.23/2.59 | % 13.23/2.59 | REDUCE: (5), (7) imply: % 13.23/2.59 | (8) $false % 13.23/2.59 | % 13.23/2.59 | CLOSE: (8) is inconsistent. % 13.23/2.59 | % 13.23/2.59 End of proof % 13.23/2.59 % SZS output end Proof for theBenchmark % 13.23/2.59 % 13.23/2.59 1982ms %------------------------------------------------------------------------------