%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM489+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 11:48:06 EDT 2023 % Result : Theorem 9.19s 2.05s % Output : Proof 12.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM489+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 16:05:24 EDT 2023 % 0.13/0.34 % 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. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.72/1.21 Prover 4: Preprocessing ... % 3.72/1.21 Prover 1: Preprocessing ... % 3.89/1.24 Prover 2: Preprocessing ... % 3.89/1.24 Prover 5: Preprocessing ... % 3.89/1.24 Prover 6: Preprocessing ... % 3.89/1.24 Prover 0: Preprocessing ... % 3.89/1.24 Prover 3: Preprocessing ... % 8.92/1.96 Prover 3: Constructing countermodel ... % 8.92/1.97 Prover 1: Constructing countermodel ... % 9.19/2.04 Prover 5: Constructing countermodel ... % 9.19/2.04 Prover 5: proved (1401ms) % 9.19/2.04 % 9.19/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.19/2.05 % 9.19/2.06 Prover 3: stopped % 9.19/2.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.19/2.06 Prover 6: Proving ... % 9.19/2.07 Prover 6: stopped % 9.19/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.19/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.24/2.14 Prover 7: Preprocessing ... % 10.24/2.15 Prover 8: Preprocessing ... % 10.64/2.17 Prover 10: Preprocessing ... % 10.64/2.20 Prover 1: Found proof (size 8) % 10.64/2.20 Prover 1: proved (1571ms) % 10.64/2.20 Prover 10: stopped % 10.64/2.21 Prover 7: stopped % 12.13/2.37 Prover 8: Warning: ignoring some quantifiers % 12.13/2.38 Prover 8: Constructing countermodel ... % 12.13/2.38 Prover 4: Constructing countermodel ... % 12.13/2.40 Prover 8: stopped % 12.58/2.42 Prover 4: stopped % 12.58/2.42 Prover 2: Proving ... % 12.58/2.43 Prover 2: stopped % 12.87/2.49 Prover 0: Proving ... % 12.87/2.49 Prover 0: stopped % 12.87/2.49 % 12.87/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.87/2.49 % 12.87/2.49 % SZS output start Proof for theBenchmark % 12.87/2.50 Assumptions after simplification: % 12.87/2.50 --------------------------------- % 12.87/2.50 % 12.87/2.50 (m__) % 12.87/2.52 $i(xr) & $i(xp) & $i(xn) & ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0 % 12.87/2.52 & $i(v0)) % 12.87/2.52 % 12.87/2.52 (m__1883) % 12.87/2.52 sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & aNaturalNumber0(xr) = 0 & % 12.87/2.52 $i(xr) & $i(xp) & $i(xn) % 12.87/2.52 % 12.87/2.52 (function-axioms) % 12.87/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.53 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 12.87/2.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.87/2.53 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 12.87/2.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.87/2.53 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 12.87/2.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.53 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 12.87/2.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.87/2.53 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 12.87/2.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.53 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 12.87/2.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 12.87/2.53 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.87/2.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 12.87/2.53 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.87/2.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 12.87/2.53 | ~ (aNaturalNumber0(v2) = v0)) % 12.87/2.53 % 12.87/2.53 Further assumptions not needed in the proof: % 12.87/2.53 -------------------------------------------- % 12.87/2.53 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 12.87/2.53 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 12.87/2.53 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 12.87/2.53 mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, % 12.87/2.53 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, % 12.87/2.53 m__1837, m__1860, m__1870, m__1894 % 12.87/2.53 % 12.87/2.53 Those formulas are unsatisfiable: % 12.87/2.53 --------------------------------- % 12.87/2.53 % 12.87/2.53 Begin of proof % 12.87/2.53 | % 12.87/2.53 | ALPHA: (m__1883) implies: % 12.87/2.54 | (1) sdtpldt0(xp, xr) = xn % 12.87/2.54 | % 12.87/2.54 | ALPHA: (m__) implies: % 12.87/2.54 | (2) ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0 & $i(v0)) % 12.87/2.54 | % 12.87/2.54 | ALPHA: (function-axioms) implies: % 12.87/2.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.87/2.54 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 12.87/2.54 | % 12.87/2.54 | DELTA: instantiating (2) with fresh symbol all_40_0 gives: % 12.87/2.54 | (4) ~ (all_40_0 = xn) & sdtpldt0(xp, xr) = all_40_0 & $i(all_40_0) % 12.87/2.54 | % 12.87/2.54 | ALPHA: (4) implies: % 12.87/2.54 | (5) ~ (all_40_0 = xn) % 12.87/2.54 | (6) sdtpldt0(xp, xr) = all_40_0 % 12.87/2.54 | % 12.87/2.54 | GROUND_INST: instantiating (3) with xn, all_40_0, xr, xp, simplifying with % 12.87/2.54 | (1), (6) gives: % 12.87/2.54 | (7) all_40_0 = xn % 12.87/2.54 | % 12.87/2.54 | REDUCE: (5), (7) imply: % 12.87/2.54 | (8) $false % 12.87/2.54 | % 12.87/2.54 | CLOSE: (8) is inconsistent. % 12.87/2.54 | % 12.87/2.54 End of proof % 12.87/2.54 % SZS output end Proof for theBenchmark % 12.87/2.54 % 12.87/2.54 1938ms %------------------------------------------------------------------------------