%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM491+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 : 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 11:48:07 EDT 2023 % Result : Theorem 12.51s 2.37s % Output : Proof 18.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM491+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % 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 14:39:12 EDT 2023 % 0.12/0.33 % CPUTime : % 0.49/0.59 ________ _____ % 0.49/0.59 ___ __ \_________(_)________________________________ % 0.49/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.59 % 0.49/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.59 (2023-06-19) % 0.49/0.59 % 0.49/0.59 (c) Philipp Rümmer, 2009-2023 % 0.49/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.59 Amanda Stjerna. % 0.49/0.59 Free software under BSD-3-Clause. % 0.49/0.59 % 0.49/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.59 % 0.49/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.61 Running up to 7 provers in parallel. % 0.49/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.49/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.49/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.49/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.49/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.49/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.49/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.55/1.22 Prover 4: Preprocessing ... % 3.55/1.22 Prover 1: Preprocessing ... % 4.14/1.26 Prover 2: Preprocessing ... % 4.14/1.26 Prover 3: Preprocessing ... % 4.14/1.27 Prover 0: Preprocessing ... % 4.14/1.27 Prover 5: Preprocessing ... % 4.14/1.27 Prover 6: Preprocessing ... % 10.11/2.03 Prover 1: Constructing countermodel ... % 10.36/2.13 Prover 6: Proving ... % 10.95/2.14 Prover 3: Constructing countermodel ... % 10.95/2.16 Prover 5: Constructing countermodel ... % 12.51/2.36 Prover 4: Constructing countermodel ... % 12.51/2.37 Prover 3: proved (1753ms) % 12.51/2.37 % 12.51/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.51/2.37 % 12.51/2.37 Prover 5: stopped % 12.51/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.51/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.51/2.38 Prover 6: stopped % 12.51/2.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.51/2.38 Prover 2: Proving ... % 12.51/2.38 Prover 2: stopped % 12.51/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.47/2.49 Prover 0: Proving ... % 13.47/2.50 Prover 7: Preprocessing ... % 13.47/2.51 Prover 0: stopped % 13.47/2.53 Prover 10: Preprocessing ... % 13.47/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.47/2.54 Prover 11: Preprocessing ... % 13.47/2.55 Prover 8: Preprocessing ... % 14.26/2.60 Prover 13: Preprocessing ... % 15.45/2.77 Prover 10: Constructing countermodel ... % 15.86/2.80 Prover 8: Warning: ignoring some quantifiers % 15.86/2.81 Prover 8: Constructing countermodel ... % 15.86/2.82 Prover 7: Constructing countermodel ... % 17.08/2.97 Prover 13: Constructing countermodel ... % 18.22/3.10 Prover 10: Found proof (size 19) % 18.22/3.10 Prover 10: proved (728ms) % 18.22/3.10 Prover 7: stopped % 18.22/3.10 Prover 4: stopped % 18.22/3.10 Prover 13: stopped % 18.22/3.10 Prover 1: stopped % 18.22/3.10 Prover 8: stopped % 18.22/3.13 Prover 11: Constructing countermodel ... % 18.22/3.15 Prover 11: stopped % 18.22/3.15 % 18.22/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.22/3.15 % 18.22/3.15 % SZS output start Proof for theBenchmark % 18.22/3.15 Assumptions after simplification: % 18.22/3.15 --------------------------------- % 18.22/3.15 % 18.22/3.15 (m__) % 18.74/3.18 $i(xp) & $i(xm) & ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~ % 18.74/3.18 doDivides0(xp, v0) & ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) | % 18.74/3.18 ~ aNaturalNumber0(v1))) % 18.74/3.18 % 18.74/3.18 (m__1837) % 18.74/3.18 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 18.74/3.18 aNaturalNumber0(xn) % 18.74/3.18 % 18.74/3.18 (m__1951) % 18.74/3.18 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.74/3.18 (sdtasdt0(xr, xm) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & % 18.74/3.18 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 18.74/3.18 % 18.74/3.18 (m__1978) % 18.74/3.18 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.74/3.18 (sdtmndt0(v2, v0) = v1 & sdtasdt0(xr, xm) = v1 & sdtasdt0(xp, xm) = v0 & % 18.74/3.18 sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 18.74/3.18 % 18.74/3.18 (function-axioms) % 18.74/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.74/3.18 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.74/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 18.74/3.18 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.74/3.18 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.74/3.18 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.74/3.18 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 18.74/3.18 % 18.74/3.18 Further assumptions not needed in the proof: % 18.74/3.18 -------------------------------------------- % 18.74/3.18 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 18.74/3.18 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 18.74/3.18 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 18.74/3.18 mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, % 18.74/3.18 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, % 18.74/3.18 m__1860, m__1870, m__1883, m__1894, m__1924 % 18.74/3.18 % 18.74/3.18 Those formulas are unsatisfiable: % 18.74/3.18 --------------------------------- % 18.74/3.18 % 18.74/3.18 Begin of proof % 18.74/3.19 | % 18.74/3.19 | ALPHA: (m__1837) implies: % 18.74/3.19 | (1) aNaturalNumber0(xm) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (m__1951) implies: % 18.74/3.19 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, xm) = v2 & % 18.74/3.19 | sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v2) = v0 % 18.74/3.19 | & $i(v2) & $i(v1) & $i(v0)) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (m__1978) implies: % 18.74/3.19 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v2, v0) = v1 & % 18.74/3.19 | sdtasdt0(xr, xm) = v1 & sdtasdt0(xp, xm) = v0 & sdtasdt0(xn, xm) = v2 % 18.74/3.19 | & sdtpldt0(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (m__) implies: % 18.74/3.19 | (4) $i(xm) % 18.74/3.19 | (5) ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~ doDivides0(xp, v0) & % 18.74/3.19 | ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) | ~ % 18.74/3.19 | aNaturalNumber0(v1))) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (function-axioms) implies: % 18.74/3.19 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.74/3.19 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.74/3.19 | % 18.74/3.19 | DELTA: instantiating (5) with fresh symbol all_42_0 gives: % 18.74/3.19 | (7) sdtasdt0(xp, xm) = all_42_0 & $i(all_42_0) & ~ doDivides0(xp, % 18.74/3.19 | all_42_0) & ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_42_0) | ~ % 18.74/3.19 | $i(v0) | ~ aNaturalNumber0(v0)) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (7) implies: % 18.74/3.19 | (8) sdtasdt0(xp, xm) = all_42_0 % 18.74/3.19 | (9) ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_42_0) | ~ $i(v0) | ~ % 18.74/3.19 | aNaturalNumber0(v0)) % 18.74/3.19 | % 18.74/3.19 | DELTA: instantiating (2) with fresh symbols all_45_0, all_45_1, all_45_2 % 18.74/3.19 | gives: % 18.74/3.19 | (10) sdtasdt0(xr, xm) = all_45_0 & sdtasdt0(xp, xm) = all_45_1 & % 18.74/3.19 | sdtasdt0(xn, xm) = all_45_2 & sdtpldt0(all_45_1, all_45_0) = all_45_2 % 18.74/3.19 | & $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (10) implies: % 18.74/3.19 | (11) sdtasdt0(xp, xm) = all_45_1 % 18.74/3.19 | % 18.74/3.19 | DELTA: instantiating (3) with fresh symbols all_47_0, all_47_1, all_47_2 % 18.74/3.19 | gives: % 18.74/3.19 | (12) sdtmndt0(all_47_0, all_47_2) = all_47_1 & sdtasdt0(xr, xm) = all_47_1 % 18.74/3.19 | & sdtasdt0(xp, xm) = all_47_2 & sdtasdt0(xn, xm) = all_47_0 & % 18.74/3.19 | sdtpldt0(all_47_2, all_47_1) = all_47_0 & $i(all_47_0) & $i(all_47_1) % 18.74/3.19 | & $i(all_47_2) % 18.74/3.19 | % 18.74/3.19 | ALPHA: (12) implies: % 18.74/3.19 | (13) sdtasdt0(xp, xm) = all_47_2 % 18.74/3.19 | % 18.74/3.20 | GROUND_INST: instantiating (6) with all_45_1, all_47_2, xm, xp, simplifying % 18.74/3.20 | with (11), (13) gives: % 18.74/3.20 | (14) all_47_2 = all_45_1 % 18.74/3.20 | % 18.74/3.20 | GROUND_INST: instantiating (6) with all_42_0, all_47_2, xm, xp, simplifying % 18.74/3.20 | with (8), (13) gives: % 18.74/3.20 | (15) all_47_2 = all_42_0 % 18.74/3.20 | % 18.74/3.20 | COMBINE_EQS: (14), (15) imply: % 18.74/3.20 | (16) all_45_1 = all_42_0 % 18.74/3.20 | % 18.74/3.20 | SIMP: (16) implies: % 18.74/3.20 | (17) all_45_1 = all_42_0 % 18.74/3.20 | % 18.74/3.20 | GROUND_INST: instantiating (9) with xm, simplifying with (1), (4), (8) gives: % 18.74/3.20 | (18) $false % 18.74/3.20 | % 18.74/3.20 | CLOSE: (18) is inconsistent. % 18.74/3.20 | % 18.74/3.20 End of proof % 18.74/3.20 % SZS output end Proof for theBenchmark % 18.74/3.20 % 18.74/3.20 2603ms %------------------------------------------------------------------------------