%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM519+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 : n002.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 9.57s 2.13s % Output : Proof 14.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM519+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n002.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 12:14:02 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.42/1.32 Prover 1: Preprocessing ... % 3.42/1.33 Prover 4: Preprocessing ... % 3.71/1.37 Prover 5: Preprocessing ... % 3.71/1.37 Prover 6: Preprocessing ... % 3.71/1.37 Prover 3: Preprocessing ... % 3.71/1.37 Prover 2: Preprocessing ... % 3.71/1.37 Prover 0: Preprocessing ... % 9.57/2.10 Prover 6: Constructing countermodel ... % 9.57/2.10 Prover 3: Constructing countermodel ... % 9.57/2.13 Prover 6: proved (1472ms) % 9.57/2.13 % 9.57/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.57/2.13 % 9.57/2.14 Prover 3: proved (1485ms) % 9.57/2.14 % 9.57/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.57/2.14 % 9.57/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.57/2.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.06/2.19 Prover 5: Constructing countermodel ... % 10.06/2.19 Prover 5: stopped % 10.37/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.37/2.21 Prover 1: Constructing countermodel ... % 10.37/2.22 Prover 7: Preprocessing ... % 10.37/2.22 Prover 8: Preprocessing ... % 10.64/2.29 Prover 10: Preprocessing ... % 11.37/2.35 Prover 2: Constructing countermodel ... % 11.37/2.35 Prover 2: stopped % 11.37/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.40/2.50 Prover 11: Preprocessing ... % 12.40/2.57 Prover 0: Constructing countermodel ... % 12.40/2.57 Prover 0: stopped % 12.40/2.57 Prover 1: Found proof (size 23) % 12.40/2.57 Prover 1: proved (1926ms) % 12.40/2.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.77/2.60 Prover 8: Warning: ignoring some quantifiers % 12.77/2.62 Prover 8: Constructing countermodel ... % 12.77/2.62 Prover 4: Constructing countermodel ... % 13.66/2.63 Prover 8: stopped % 13.66/2.64 Prover 7: Constructing countermodel ... % 13.66/2.65 Prover 11: stopped % 13.66/2.66 Prover 4: stopped % 13.66/2.67 Prover 7: stopped % 13.66/2.67 Prover 13: Preprocessing ... % 13.66/2.68 Prover 10: Constructing countermodel ... % 13.66/2.70 Prover 10: stopped % 14.25/2.73 Prover 13: stopped % 14.25/2.73 % 14.25/2.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.25/2.73 % 14.25/2.73 % SZS output start Proof for theBenchmark % 14.25/2.74 Assumptions after simplification: % 14.25/2.74 --------------------------------- % 14.25/2.74 % 14.25/2.74 (m__2449) % 14.25/2.76 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = % 14.25/2.76 v1 & doDivides0(xr, xn) = v0 & ((v1 = 0 & ? [v2: $i] : (sdtasdt0(xr, v2) = % 14.25/2.76 xm & aNaturalNumber0(v2) = 0 & $i(v2))) | (v0 = 0 & ? [v2: $i] : % 14.25/2.76 (sdtasdt0(xr, v2) = xn & aNaturalNumber0(v2) = 0 & $i(v2))))) % 14.25/2.77 % 14.25/2.77 (m__2487) % 14.25/2.77 $i(xr) & $i(xn) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0 & ! % 14.25/2.77 [v1: $i] : ( ~ (sdtasdt0(xr, v1) = xn) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 % 14.25/2.77 = 0) & aNaturalNumber0(v1) = v2))) % 14.25/2.77 % 14.25/2.77 (m__2698) % 14.25/2.77 $i(xr) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0 & ! % 14.25/2.77 [v1: $i] : ( ~ (sdtasdt0(xr, v1) = xm) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 % 14.25/2.77 = 0) & aNaturalNumber0(v1) = v2))) % 14.25/2.77 % 14.25/2.77 (function-axioms) % 14.25/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.77 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 14.25/2.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.25/2.77 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 14.25/2.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.25/2.77 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 14.25/2.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.77 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 14.25/2.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.25/2.77 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 14.25/2.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.77 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 14.25/2.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 14.25/2.77 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 14.25/2.77 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 14.25/2.77 | ~ (aNaturalNumber0(v2) = v0)) % 14.25/2.77 % 14.25/2.77 Further assumptions not needed in the proof: % 14.25/2.77 -------------------------------------------- % 14.25/2.77 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 14.25/2.77 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 14.25/2.77 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 14.25/2.77 mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, % 14.25/2.77 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__1799, % 14.25/2.77 m__1837, m__1860, m__1870, m__2075, m__2287, m__2306, m__2315, m__2327, m__2342, % 14.25/2.77 m__2362, m__2377 % 14.25/2.77 % 14.25/2.77 Those formulas are unsatisfiable: % 14.25/2.77 --------------------------------- % 14.25/2.77 % 14.25/2.77 Begin of proof % 14.25/2.78 | % 14.25/2.78 | ALPHA: (m__2449) implies: % 14.25/2.78 | (1) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & doDivides0(xr, % 14.25/2.78 | xn) = v0 & ((v1 = 0 & ? [v2: $i] : (sdtasdt0(xr, v2) = xm & % 14.25/2.78 | aNaturalNumber0(v2) = 0 & $i(v2))) | (v0 = 0 & ? [v2: $i] : % 14.25/2.78 | (sdtasdt0(xr, v2) = xn & aNaturalNumber0(v2) = 0 & $i(v2))))) % 14.25/2.78 | % 14.25/2.78 | ALPHA: (m__2487) implies: % 14.25/2.78 | (2) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xn) = v0 & ! [v1: $i] : ( % 14.25/2.78 | ~ (sdtasdt0(xr, v1) = xn) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) % 14.25/2.78 | & aNaturalNumber0(v1) = v2))) % 14.25/2.78 | % 14.25/2.78 | ALPHA: (m__2698) implies: % 14.25/2.78 | (3) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xr, xm) = v0 & ! [v1: $i] : ( % 14.25/2.78 | ~ (sdtasdt0(xr, v1) = xm) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) % 14.25/2.78 | & aNaturalNumber0(v1) = v2))) % 14.25/2.78 | % 14.25/2.78 | ALPHA: (function-axioms) implies: % 14.25/2.78 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.25/2.78 | ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 14.25/2.78 | (doDivides0(v3, v2) = v0)) % 14.25/2.78 | % 14.25/2.78 | DELTA: instantiating (2) with fresh symbol all_49_0 gives: % 14.25/2.78 | (5) ~ (all_49_0 = 0) & doDivides0(xr, xn) = all_49_0 & ! [v0: $i] : ( ~ % 14.25/2.78 | (sdtasdt0(xr, v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 14.25/2.78 | aNaturalNumber0(v0) = v1)) % 14.25/2.78 | % 14.25/2.78 | ALPHA: (5) implies: % 14.25/2.78 | (6) ~ (all_49_0 = 0) % 14.25/2.78 | (7) doDivides0(xr, xn) = all_49_0 % 14.25/2.78 | % 14.25/2.78 | DELTA: instantiating (3) with fresh symbol all_58_0 gives: % 14.25/2.78 | (8) ~ (all_58_0 = 0) & doDivides0(xr, xm) = all_58_0 & ! [v0: $i] : ( ~ % 14.25/2.78 | (sdtasdt0(xr, v0) = xm) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 14.25/2.78 | aNaturalNumber0(v0) = v1)) % 14.25/2.79 | % 14.25/2.79 | ALPHA: (8) implies: % 14.25/2.79 | (9) ~ (all_58_0 = 0) % 14.25/2.79 | (10) doDivides0(xr, xm) = all_58_0 % 14.25/2.79 | % 14.25/2.79 | DELTA: instantiating (1) with fresh symbols all_63_0, all_63_1 gives: % 14.25/2.79 | (11) doDivides0(xr, xm) = all_63_0 & doDivides0(xr, xn) = all_63_1 & % 14.25/2.79 | ((all_63_0 = 0 & ? [v0: $i] : (sdtasdt0(xr, v0) = xm & % 14.25/2.79 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_63_1 = 0 & ? [v0: $i] % 14.25/2.79 | : (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)))) % 14.25/2.79 | % 14.25/2.79 | ALPHA: (11) implies: % 14.25/2.79 | (12) doDivides0(xr, xn) = all_63_1 % 14.25/2.79 | (13) doDivides0(xr, xm) = all_63_0 % 14.25/2.79 | (14) (all_63_0 = 0 & ? [v0: $i] : (sdtasdt0(xr, v0) = xm & % 14.25/2.79 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_63_1 = 0 & ? [v0: $i] : % 14.25/2.79 | (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0))) % 14.25/2.79 | % 14.25/2.79 | GROUND_INST: instantiating (4) with all_49_0, all_63_1, xn, xr, simplifying % 14.25/2.79 | with (7), (12) gives: % 14.25/2.79 | (15) all_63_1 = all_49_0 % 14.25/2.79 | % 14.25/2.79 | GROUND_INST: instantiating (4) with all_58_0, all_63_0, xm, xr, simplifying % 14.25/2.79 | with (10), (13) gives: % 14.25/2.79 | (16) all_63_0 = all_58_0 % 14.25/2.79 | % 14.25/2.79 | BETA: splitting (14) gives: % 14.25/2.79 | % 14.25/2.79 | Case 1: % 14.25/2.79 | | % 14.25/2.79 | | (17) all_63_0 = 0 & ? [v0: $i] : (sdtasdt0(xr, v0) = xm & % 14.25/2.79 | | aNaturalNumber0(v0) = 0 & $i(v0)) % 14.25/2.79 | | % 14.25/2.79 | | ALPHA: (17) implies: % 14.25/2.79 | | (18) all_63_0 = 0 % 14.25/2.79 | | % 14.25/2.79 | | COMBINE_EQS: (16), (18) imply: % 14.25/2.79 | | (19) all_58_0 = 0 % 14.25/2.79 | | % 14.25/2.79 | | SIMP: (19) implies: % 14.25/2.79 | | (20) all_58_0 = 0 % 14.25/2.79 | | % 14.25/2.79 | | REDUCE: (9), (20) imply: % 14.25/2.79 | | (21) $false % 14.25/2.79 | | % 14.25/2.79 | | CLOSE: (21) is inconsistent. % 14.25/2.79 | | % 14.25/2.79 | Case 2: % 14.25/2.79 | | % 14.25/2.79 | | (22) all_63_1 = 0 & ? [v0: $i] : (sdtasdt0(xr, v0) = xn & % 14.25/2.79 | | aNaturalNumber0(v0) = 0 & $i(v0)) % 14.56/2.79 | | % 14.56/2.79 | | ALPHA: (22) implies: % 14.56/2.79 | | (23) all_63_1 = 0 % 14.56/2.79 | | % 14.56/2.79 | | COMBINE_EQS: (15), (23) imply: % 14.56/2.79 | | (24) all_49_0 = 0 % 14.56/2.79 | | % 14.56/2.79 | | SIMP: (24) implies: % 14.56/2.79 | | (25) all_49_0 = 0 % 14.56/2.79 | | % 14.56/2.79 | | REDUCE: (6), (25) imply: % 14.56/2.79 | | (26) $false % 14.56/2.79 | | % 14.56/2.79 | | CLOSE: (26) is inconsistent. % 14.56/2.79 | | % 14.56/2.79 | End of split % 14.56/2.79 | % 14.56/2.79 End of proof % 14.56/2.79 % SZS output end Proof for theBenchmark % 14.56/2.79 % 14.56/2.79 2174ms %------------------------------------------------------------------------------