%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM491+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 : n017.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 11:48:07 EDT 2023 % Result : Theorem 12.46s 2.42s % Output : Proof 18.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM491+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.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 13:04:55 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.19/1.21 Prover 1: Preprocessing ... % 3.19/1.21 Prover 4: Preprocessing ... % 3.82/1.24 Prover 2: Preprocessing ... % 3.82/1.24 Prover 0: Preprocessing ... % 3.82/1.24 Prover 6: Preprocessing ... % 3.82/1.24 Prover 3: Preprocessing ... % 3.82/1.24 Prover 5: Preprocessing ... % 8.43/1.95 Prover 1: Constructing countermodel ... % 8.43/1.96 Prover 3: Constructing countermodel ... % 9.75/2.07 Prover 6: Proving ... % 10.19/2.13 Prover 5: Constructing countermodel ... % 11.41/2.28 Prover 4: Constructing countermodel ... % 11.41/2.28 Prover 2: Proving ... % 12.46/2.41 Prover 3: proved (1770ms) % 12.46/2.42 % 12.46/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.46/2.42 % 12.46/2.42 Prover 5: stopped % 12.46/2.43 Prover 6: stopped % 12.46/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.46/2.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.46/2.44 Prover 2: stopped % 12.46/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.87/2.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.92/2.45 Prover 0: Proving ... % 12.92/2.46 Prover 0: stopped % 12.92/2.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.32/2.58 Prover 10: Preprocessing ... % 13.32/2.58 Prover 13: Preprocessing ... % 13.32/2.60 Prover 8: Preprocessing ... % 13.32/2.61 Prover 11: Preprocessing ... % 13.32/2.62 Prover 7: Preprocessing ... % 15.52/2.81 Prover 10: Constructing countermodel ... % 15.52/2.84 Prover 8: Warning: ignoring some quantifiers % 15.52/2.84 Prover 13: Constructing countermodel ... % 15.94/2.85 Prover 8: Constructing countermodel ... % 15.97/2.86 Prover 7: Constructing countermodel ... % 17.86/3.13 Prover 11: Constructing countermodel ... % 18.38/3.18 Prover 10: Found proof (size 23) % 18.38/3.18 Prover 10: proved (738ms) % 18.38/3.18 Prover 13: stopped % 18.38/3.18 Prover 4: stopped % 18.38/3.18 Prover 8: stopped % 18.38/3.18 Prover 7: stopped % 18.38/3.18 Prover 11: stopped % 18.38/3.18 Prover 1: stopped % 18.38/3.18 % 18.38/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.38/3.18 % 18.38/3.19 % SZS output start Proof for theBenchmark % 18.38/3.19 Assumptions after simplification: % 18.38/3.19 --------------------------------- % 18.38/3.19 % 18.38/3.19 (mDefDiv) % 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 18.38/3.22 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 18.38/3.22 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 18.38/3.22 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 18.38/3.22 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 18.38/3.22 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 18.38/3.22 % 18.38/3.22 (mMulComm) % 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 18.38/3.22 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 18.38/3.22 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 18.38/3.22 % 18.38/3.22 (mSortsB_02) % 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 18.38/3.22 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 18.38/3.22 aNaturalNumber0(v2)) % 18.38/3.22 % 18.38/3.22 (m__) % 18.38/3.23 $i(xp) & $i(xm) & ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~ % 18.38/3.23 doDivides0(xp, v0)) % 18.38/3.23 % 18.38/3.23 (m__1837) % 18.38/3.23 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 18.38/3.23 aNaturalNumber0(xn) % 18.38/3.23 % 18.38/3.23 (m__1951) % 18.38/3.23 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.38/3.23 (sdtasdt0(xr, xm) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & % 18.38/3.23 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 18.38/3.23 % 18.38/3.23 (m__1978) % 18.38/3.23 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.38/3.23 (sdtmndt0(v1, v2) = v0 & sdtasdt0(xr, xm) = v0 & sdtasdt0(xp, xm) = v2 & % 18.38/3.23 sdtasdt0(xn, xm) = v1 & $i(v2) & $i(v1) & $i(v0)) % 18.38/3.23 % 18.38/3.23 (function-axioms) % 18.38/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.38/3.23 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.38/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 18.38/3.23 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.38/3.23 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.38/3.23 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.38/3.23 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 18.38/3.23 % 18.38/3.23 Further assumptions not needed in the proof: % 18.38/3.23 -------------------------------------------- % 18.38/3.23 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefPrime, mDefQuot, % 18.38/3.23 mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, % 18.38/3.23 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, % 18.38/3.23 mNatSort, mPrimDiv, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, % 18.38/3.23 m_MulUnit, m_MulZero, m__1799, m__1860, m__1870, m__1883, m__1894, m__1924 % 18.38/3.23 % 18.38/3.23 Those formulas are unsatisfiable: % 18.38/3.23 --------------------------------- % 18.38/3.23 % 18.38/3.23 Begin of proof % 18.38/3.23 | % 18.38/3.23 | ALPHA: (mDefDiv) implies: % 18.38/3.23 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | % 18.38/3.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 18.38/3.23 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) % 18.38/3.23 | % 18.38/3.23 | ALPHA: (m__1837) implies: % 18.38/3.23 | (2) aNaturalNumber0(xm) % 18.38/3.23 | (3) aNaturalNumber0(xp) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (m__1951) implies: % 18.38/3.24 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, xm) = v2 & % 18.38/3.24 | sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v2) = v0 % 18.38/3.24 | & $i(v2) & $i(v1) & $i(v0)) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (m__1978) implies: % 18.38/3.24 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v1, v2) = v0 & % 18.38/3.24 | sdtasdt0(xr, xm) = v0 & sdtasdt0(xp, xm) = v2 & sdtasdt0(xn, xm) = v1 % 18.38/3.24 | & $i(v2) & $i(v1) & $i(v0)) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (m__) implies: % 18.38/3.24 | (6) $i(xm) % 18.38/3.24 | (7) $i(xp) % 18.38/3.24 | (8) ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~ doDivides0(xp, v0)) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (function-axioms) implies: % 18.38/3.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.38/3.24 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.38/3.24 | % 18.38/3.24 | DELTA: instantiating (8) with fresh symbol all_38_0 gives: % 18.38/3.24 | (10) sdtasdt0(xp, xm) = all_38_0 & $i(all_38_0) & ~ doDivides0(xp, % 18.38/3.24 | all_38_0) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (10) implies: % 18.38/3.24 | (11) ~ doDivides0(xp, all_38_0) % 18.38/3.24 | (12) sdtasdt0(xp, xm) = all_38_0 % 18.38/3.24 | % 18.38/3.24 | DELTA: instantiating (4) with fresh symbols all_42_0, all_42_1, all_42_2 % 18.38/3.24 | gives: % 18.38/3.24 | (13) sdtasdt0(xr, xm) = all_42_0 & sdtasdt0(xp, xm) = all_42_1 & % 18.38/3.24 | sdtasdt0(xn, xm) = all_42_2 & sdtpldt0(all_42_1, all_42_0) = all_42_2 % 18.38/3.24 | & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (13) implies: % 18.38/3.24 | (14) sdtasdt0(xp, xm) = all_42_1 % 18.38/3.24 | % 18.38/3.24 | DELTA: instantiating (5) with fresh symbols all_44_0, all_44_1, all_44_2 % 18.38/3.24 | gives: % 18.38/3.24 | (15) sdtmndt0(all_44_1, all_44_0) = all_44_2 & sdtasdt0(xr, xm) = all_44_2 % 18.38/3.24 | & sdtasdt0(xp, xm) = all_44_0 & sdtasdt0(xn, xm) = all_44_1 & % 18.38/3.24 | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (15) implies: % 18.38/3.24 | (16) sdtasdt0(xp, xm) = all_44_0 % 18.38/3.24 | % 18.38/3.24 | GROUND_INST: instantiating (9) with all_42_1, all_44_0, xm, xp, simplifying % 18.38/3.24 | with (14), (16) gives: % 18.38/3.24 | (17) all_44_0 = all_42_1 % 18.38/3.24 | % 18.38/3.24 | GROUND_INST: instantiating (9) with all_38_0, all_44_0, xm, xp, simplifying % 18.38/3.24 | with (12), (16) gives: % 18.38/3.24 | (18) all_44_0 = all_38_0 % 18.38/3.24 | % 18.38/3.24 | COMBINE_EQS: (17), (18) imply: % 18.38/3.24 | (19) all_42_1 = all_38_0 % 18.38/3.24 | % 18.38/3.24 | SIMP: (19) implies: % 18.38/3.24 | (20) all_42_1 = all_38_0 % 18.38/3.24 | % 18.38/3.24 | GROUND_INST: instantiating (mSortsB_02) with xp, xm, all_38_0, simplifying % 18.38/3.24 | with (2), (3), (6), (7), (12) gives: % 18.38/3.24 | (21) aNaturalNumber0(all_38_0) % 18.38/3.24 | % 18.38/3.24 | GROUND_INST: instantiating (mMulComm) with xp, xm, all_38_0, simplifying with % 18.38/3.24 | (2), (3), (6), (7), (12) gives: % 18.38/3.24 | (22) sdtasdt0(xm, xp) = all_38_0 & $i(all_38_0) % 18.38/3.24 | % 18.38/3.24 | ALPHA: (22) implies: % 18.38/3.24 | (23) $i(all_38_0) % 18.38/3.24 | % 18.38/3.25 | GROUND_INST: instantiating (1) with xp, all_38_0, xm, simplifying with (2), % 18.38/3.25 | (3), (6), (7), (11), (12), (21), (23) gives: % 18.38/3.25 | (24) $false % 18.38/3.25 | % 18.38/3.25 | CLOSE: (24) is inconsistent. % 18.38/3.25 | % 18.38/3.25 End of proof % 18.38/3.25 % SZS output end Proof for theBenchmark % 18.38/3.25 % 18.38/3.25 2637ms %------------------------------------------------------------------------------