%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM530+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 : n019.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 11:48:24 EDT 2023 % Result : Theorem 6.84s 1.69s % Output : Proof 11.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM530+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n019.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 10:05:13 EDT 2023 % 0.12/0.33 % CPUTime : % 0.17/0.59 ________ _____ % 0.17/0.59 ___ __ \_________(_)________________________________ % 0.17/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.59 % 0.17/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.59 (2023-06-19) % 0.17/0.59 % 0.17/0.59 (c) Philipp Rümmer, 2009-2023 % 0.17/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.59 Amanda Stjerna. % 0.17/0.59 Free software under BSD-3-Clause. % 0.17/0.59 % 0.17/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.59 % 0.17/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.60 Running up to 7 provers in parallel. % 0.17/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.65/1.20 Prover 1: Preprocessing ... % 3.65/1.20 Prover 4: Preprocessing ... % 3.65/1.24 Prover 5: Preprocessing ... % 3.65/1.24 Prover 0: Preprocessing ... % 3.65/1.24 Prover 3: Preprocessing ... % 3.65/1.24 Prover 2: Preprocessing ... % 3.65/1.24 Prover 6: Preprocessing ... % 6.84/1.64 Prover 3: Constructing countermodel ... % 6.84/1.64 Prover 6: Constructing countermodel ... % 6.84/1.69 Prover 6: proved (1070ms) % 6.84/1.69 % 6.84/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.84/1.69 % 7.28/1.70 Prover 3: stopped % 7.28/1.70 Prover 0: stopped % 7.28/1.71 Prover 5: Constructing countermodel ... % 7.28/1.71 Prover 5: stopped % 7.28/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.28/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.28/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.28/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.78/1.76 Prover 2: Constructing countermodel ... % 7.78/1.76 Prover 2: stopped % 7.78/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.33/1.85 Prover 1: Constructing countermodel ... % 8.33/1.88 Prover 7: Preprocessing ... % 8.33/1.89 Prover 8: Preprocessing ... % 8.33/1.89 Prover 10: Preprocessing ... % 8.33/1.91 Prover 13: Preprocessing ... % 8.33/1.93 Prover 11: Preprocessing ... % 9.06/2.05 Prover 1: Found proof (size 8) % 9.06/2.05 Prover 1: proved (1443ms) % 9.06/2.06 Prover 11: stopped % 9.06/2.07 Prover 8: Warning: ignoring some quantifiers % 9.06/2.10 Prover 8: Constructing countermodel ... % 9.06/2.12 Prover 10: Constructing countermodel ... % 9.06/2.13 Prover 8: stopped % 9.06/2.14 Prover 10: stopped % 9.99/2.16 Prover 7: Constructing countermodel ... % 9.99/2.17 Prover 13: Constructing countermodel ... % 9.99/2.18 Prover 7: stopped % 9.99/2.19 Prover 13: stopped % 11.04/2.22 Prover 4: Constructing countermodel ... % 11.04/2.24 Prover 4: stopped % 11.04/2.25 % 11.04/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.04/2.25 % 11.04/2.25 % SZS output start Proof for theBenchmark % 11.04/2.25 Assumptions after simplification: % 11.04/2.25 --------------------------------- % 11.04/2.25 % 11.04/2.25 (m__3025) % 11.04/2.27 isPrime0(xp) = 0 & $i(xp) % 11.04/2.27 % 11.04/2.27 (m__3161) % 11.04/2.27 $i(xp) & ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xp) = v0) % 11.04/2.27 % 11.04/2.27 (function-axioms) % 11.04/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.04/2.28 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 11.04/2.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.04/2.28 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 11.04/2.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.04/2.28 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 11.04/2.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.04/2.28 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 11.04/2.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.04/2.28 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 11.04/2.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.04/2.28 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 11.04/2.28 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 11.04/2.28 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.04/2.28 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 11.04/2.28 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.04/2.28 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 11.04/2.28 | ~ (aNaturalNumber0(v2) = v0)) % 11.04/2.28 % 11.04/2.28 Further assumptions not needed in the proof: % 11.04/2.28 -------------------------------------------- % 11.04/2.28 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 11.04/2.28 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 11.04/2.28 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 11.04/2.28 mMulCanc, mMulComm, mNatSort, mPDP, mPrimDiv, mSortsB, mSortsB_02, mSortsC, % 11.04/2.28 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__2963, % 11.04/2.28 m__2987, m__3014, m__3046, m__3059, m__3082, m__3124 % 11.04/2.28 % 11.04/2.28 Those formulas are unsatisfiable: % 11.04/2.28 --------------------------------- % 11.04/2.28 % 11.04/2.28 Begin of proof % 11.04/2.28 | % 11.04/2.28 | ALPHA: (m__3025) implies: % 11.04/2.29 | (1) isPrime0(xp) = 0 % 11.04/2.29 | % 11.04/2.29 | ALPHA: (m__3161) implies: % 11.04/2.29 | (2) ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xp) = v0) % 11.04/2.29 | % 11.04/2.29 | ALPHA: (function-axioms) implies: % 11.04/2.29 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.04/2.29 | (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) % 11.04/2.29 | % 11.04/2.29 | DELTA: instantiating (2) with fresh symbol all_40_0 gives: % 11.04/2.29 | (4) ~ (all_40_0 = 0) & isPrime0(xp) = all_40_0 % 11.04/2.29 | % 11.04/2.29 | ALPHA: (4) implies: % 11.04/2.29 | (5) ~ (all_40_0 = 0) % 11.04/2.29 | (6) isPrime0(xp) = all_40_0 % 11.04/2.29 | % 11.04/2.29 | GROUND_INST: instantiating (3) with 0, all_40_0, xp, simplifying with (1), (6) % 11.04/2.29 | gives: % 11.04/2.29 | (7) all_40_0 = 0 % 11.04/2.29 | % 11.04/2.29 | REDUCE: (5), (7) imply: % 11.04/2.29 | (8) $false % 11.04/2.29 | % 11.04/2.29 | CLOSE: (8) is inconsistent. % 11.04/2.29 | % 11.04/2.29 End of proof % 11.04/2.29 % SZS output end Proof for theBenchmark % 11.04/2.29 % 11.04/2.29 1707ms %------------------------------------------------------------------------------