%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM519+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 : n023.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 11:48:20 EDT 2023 % Result : Theorem 8.49s 1.85s % Output : Proof 12.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM519+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.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 15:16:41 EDT 2023 % 0.12/0.34 % CPUTime : % 0.62/0.60 ________ _____ % 0.62/0.60 ___ __ \_________(_)________________________________ % 0.62/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.60 % 0.62/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.60 (2023-06-19) % 0.62/0.60 % 0.62/0.60 (c) Philipp Rümmer, 2009-2023 % 0.62/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.60 Amanda Stjerna. % 0.62/0.60 Free software under BSD-3-Clause. % 0.62/0.60 % 0.62/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.60 % 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.62/0.61 Running up to 7 provers in parallel. % 0.62/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.42/1.17 Prover 4: Preprocessing ... % 3.42/1.17 Prover 1: Preprocessing ... % 3.88/1.21 Prover 2: Preprocessing ... % 3.88/1.21 Prover 6: Preprocessing ... % 3.88/1.21 Prover 5: Preprocessing ... % 3.88/1.21 Prover 3: Preprocessing ... % 3.88/1.21 Prover 0: Preprocessing ... % 7.82/1.79 Prover 6: Constructing countermodel ... % 7.82/1.79 Prover 3: Constructing countermodel ... % 8.49/1.84 Prover 3: proved (1218ms) % 8.49/1.84 Prover 6: proved (1214ms) % 8.49/1.84 % 8.49/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.49/1.85 % 8.49/1.85 % 8.49/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.49/1.85 % 8.49/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.49/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.49/1.85 Prover 5: Constructing countermodel ... % 8.49/1.85 Prover 5: stopped % 8.49/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.07/1.94 Prover 1: Constructing countermodel ... % 9.07/1.96 Prover 7: Preprocessing ... % 9.65/1.98 Prover 8: Preprocessing ... % 9.65/1.98 Prover 10: Preprocessing ... % 10.67/2.16 Prover 2: Constructing countermodel ... % 10.67/2.16 Prover 2: stopped % 10.67/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.28/2.21 Prover 1: Found proof (size 20) % 11.28/2.22 Prover 1: proved (1595ms) % 11.28/2.26 Prover 10: Constructing countermodel ... % 11.28/2.27 Prover 11: Preprocessing ... % 11.28/2.27 Prover 8: Warning: ignoring some quantifiers % 12.00/2.29 Prover 8: Constructing countermodel ... % 12.08/2.30 Prover 0: Constructing countermodel ... % 12.08/2.30 Prover 0: stopped % 12.08/2.30 Prover 10: stopped % 12.08/2.30 Prover 8: stopped % 12.19/2.31 Prover 7: Constructing countermodel ... % 12.22/2.33 Prover 7: stopped % 12.22/2.34 Prover 11: stopped % 12.22/2.35 Prover 4: Constructing countermodel ... % 12.22/2.37 Prover 4: stopped % 12.22/2.37 % 12.22/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.22/2.37 % 12.22/2.38 % SZS output start Proof for theBenchmark % 12.22/2.38 Assumptions after simplification: % 12.22/2.38 --------------------------------- % 12.22/2.38 % 12.22/2.38 (m__2449) % 12.22/2.41 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = % 12.22/2.41 v1 & doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0)) % 12.22/2.41 % 12.22/2.41 (m__2487) % 12.74/2.41 $i(xr) & $i(xn) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0) % 12.74/2.41 % 12.74/2.41 (m__2698) % 12.74/2.41 $i(xr) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0) % 12.74/2.41 % 12.74/2.41 (function-axioms) % 12.74/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.74/2.42 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 12.74/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.74/2.42 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 12.74/2.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.74/2.42 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 12.74/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.74/2.42 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 12.74/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.74/2.42 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 12.74/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.74/2.42 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 12.74/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 12.74/2.42 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.74/2.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 12.74/2.42 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.74/2.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 12.74/2.42 | ~ (aNaturalNumber0(v2) = v0)) % 12.74/2.42 % 12.74/2.42 Further assumptions not needed in the proof: % 12.74/2.42 -------------------------------------------- % 12.74/2.42 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 12.74/2.42 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 12.74/2.42 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 12.74/2.42 mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, % 12.74/2.42 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__1799, % 12.74/2.42 m__1837, m__1860, m__1870, m__2075, m__2287, m__2306, m__2315, m__2327, m__2342, % 12.74/2.42 m__2362, m__2377 % 12.74/2.42 % 12.74/2.42 Those formulas are unsatisfiable: % 12.74/2.42 --------------------------------- % 12.74/2.42 % 12.74/2.42 Begin of proof % 12.74/2.42 | % 12.74/2.42 | ALPHA: (m__2449) implies: % 12.74/2.42 | (1) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & doDivides0(xr, % 12.74/2.42 | xn) = v0 & (v1 = 0 | v0 = 0)) % 12.74/2.42 | % 12.74/2.42 | ALPHA: (m__2487) implies: % 12.74/2.42 | (2) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0) % 12.74/2.42 | % 12.74/2.42 | ALPHA: (m__2698) implies: % 12.74/2.42 | (3) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0) % 12.74/2.42 | % 12.74/2.42 | ALPHA: (function-axioms) implies: % 12.74/2.43 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.74/2.43 | ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 12.74/2.43 | (doDivides0(v3, v2) = v0)) % 12.74/2.43 | % 12.74/2.43 | DELTA: instantiating (2) with fresh symbol all_38_0 gives: % 12.74/2.43 | (5) ~ (all_38_0 = 0) & doDivides0(xr, xn) = all_38_0 % 12.74/2.43 | % 12.74/2.43 | ALPHA: (5) implies: % 12.74/2.43 | (6) ~ (all_38_0 = 0) % 12.74/2.43 | (7) doDivides0(xr, xn) = all_38_0 % 12.74/2.43 | % 12.74/2.43 | DELTA: instantiating (3) with fresh symbol all_40_0 gives: % 12.74/2.43 | (8) ~ (all_40_0 = 0) & doDivides0(xr, xm) = all_40_0 % 12.74/2.43 | % 12.74/2.43 | ALPHA: (8) implies: % 12.74/2.43 | (9) ~ (all_40_0 = 0) % 12.74/2.43 | (10) doDivides0(xr, xm) = all_40_0 % 12.74/2.43 | % 12.74/2.43 | DELTA: instantiating (1) with fresh symbols all_48_0, all_48_1 gives: % 12.74/2.43 | (11) doDivides0(xr, xm) = all_48_0 & doDivides0(xr, xn) = all_48_1 & % 12.74/2.43 | (all_48_0 = 0 | all_48_1 = 0) % 12.74/2.43 | % 12.74/2.43 | ALPHA: (11) implies: % 12.74/2.43 | (12) doDivides0(xr, xn) = all_48_1 % 12.74/2.43 | (13) doDivides0(xr, xm) = all_48_0 % 12.74/2.43 | (14) all_48_0 = 0 | all_48_1 = 0 % 12.74/2.43 | % 12.74/2.43 | GROUND_INST: instantiating (4) with all_38_0, all_48_1, xn, xr, simplifying % 12.74/2.43 | with (7), (12) gives: % 12.74/2.43 | (15) all_48_1 = all_38_0 % 12.74/2.43 | % 12.74/2.43 | GROUND_INST: instantiating (4) with all_40_0, all_48_0, xm, xr, simplifying % 12.74/2.43 | with (10), (13) gives: % 12.74/2.43 | (16) all_48_0 = all_40_0 % 12.74/2.43 | % 12.74/2.43 | BETA: splitting (14) gives: % 12.74/2.43 | % 12.74/2.43 | Case 1: % 12.74/2.43 | | % 12.74/2.43 | | (17) all_48_0 = 0 % 12.74/2.43 | | % 12.74/2.43 | | COMBINE_EQS: (16), (17) imply: % 12.74/2.43 | | (18) all_40_0 = 0 % 12.74/2.43 | | % 12.74/2.43 | | SIMP: (18) implies: % 12.74/2.43 | | (19) all_40_0 = 0 % 12.74/2.43 | | % 12.74/2.43 | | REDUCE: (9), (19) imply: % 12.74/2.43 | | (20) $false % 12.74/2.43 | | % 12.74/2.43 | | CLOSE: (20) is inconsistent. % 12.74/2.43 | | % 12.74/2.43 | Case 2: % 12.74/2.43 | | % 12.74/2.43 | | (21) all_48_1 = 0 % 12.74/2.43 | | % 12.74/2.43 | | COMBINE_EQS: (15), (21) imply: % 12.74/2.43 | | (22) all_38_0 = 0 % 12.74/2.44 | | % 12.74/2.44 | | REDUCE: (6), (22) imply: % 12.74/2.44 | | (23) $false % 12.74/2.44 | | % 12.74/2.44 | | CLOSE: (23) is inconsistent. % 12.74/2.44 | | % 12.74/2.44 | End of split % 12.74/2.44 | % 12.74/2.44 End of proof % 12.74/2.44 % SZS output end Proof for theBenchmark % 12.74/2.44 % 12.74/2.44 1833ms %------------------------------------------------------------------------------