%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM521+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 : n004.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 11:48:21 EDT 2023 % Result : Theorem 11.99s 2.42s % Output : Proof 21.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM521+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 : n004.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 16:59:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.77/1.26 Prover 4: Preprocessing ... % 3.77/1.27 Prover 1: Preprocessing ... % 3.77/1.32 Prover 0: Preprocessing ... % 3.77/1.32 Prover 5: Preprocessing ... % 3.77/1.32 Prover 2: Preprocessing ... % 3.77/1.32 Prover 3: Preprocessing ... % 3.77/1.32 Prover 6: Preprocessing ... % 9.68/2.11 Prover 3: Constructing countermodel ... % 9.68/2.11 Prover 6: Proving ... % 9.68/2.12 Prover 1: Constructing countermodel ... % 10.49/2.20 Prover 5: Constructing countermodel ... % 11.99/2.41 Prover 2: Proving ... % 11.99/2.42 Prover 3: proved (1799ms) % 11.99/2.42 % 11.99/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.99/2.42 % 11.99/2.43 Prover 5: stopped % 12.54/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.54/2.43 Prover 6: stopped % 12.54/2.44 Prover 2: stopped % 12.54/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.54/2.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.54/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.79/2.51 Prover 4: Constructing countermodel ... % 13.26/2.56 Prover 8: Preprocessing ... % 13.26/2.58 Prover 7: Preprocessing ... % 13.26/2.61 Prover 0: Proving ... % 13.26/2.62 Prover 0: stopped % 13.26/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.26/2.63 Prover 10: Preprocessing ... % 13.26/2.64 Prover 11: Preprocessing ... % 14.61/2.72 Prover 13: Preprocessing ... % 14.87/2.81 Prover 8: Warning: ignoring some quantifiers % 14.87/2.82 Prover 8: Constructing countermodel ... % 15.86/2.89 Prover 10: Constructing countermodel ... % 16.51/2.97 Prover 7: Constructing countermodel ... % 17.14/3.10 Prover 13: Constructing countermodel ... % 18.14/3.21 Prover 11: Constructing countermodel ... % 21.27/3.60 Prover 7: Found proof (size 33) % 21.27/3.60 Prover 7: proved (1176ms) % 21.27/3.60 Prover 13: stopped % 21.27/3.60 Prover 4: stopped % 21.27/3.60 Prover 10: stopped % 21.27/3.60 Prover 11: stopped % 21.27/3.60 Prover 8: stopped % 21.27/3.60 Prover 1: stopped % 21.27/3.60 % 21.27/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.27/3.60 % 21.27/3.61 % SZS output start Proof for theBenchmark % 21.27/3.61 Assumptions after simplification: % 21.27/3.61 --------------------------------- % 21.27/3.61 % 21.27/3.61 (mDefPrime) % 21.27/3.62 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 21.27/3.62 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 21.27/3.62 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 21.27/3.62 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 21.27/3.62 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 21.27/3.62 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 21.27/3.62 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 21.27/3.62 % 21.27/3.62 (mLETotal) % 21.27/3.62 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 21.27/3.62 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 21.27/3.62 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 21.27/3.62 % 21.27/3.62 (mSortsC_01) % 21.27/3.62 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 21.27/3.62 % 21.27/3.62 (m__) % 21.27/3.64 $i(xp) & $i(xm) & $i(xn) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & ! % 21.27/3.64 [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xm) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & % 21.27/3.64 ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ~ % 21.27/3.64 aNaturalNumber0(v0)) % 21.27/3.64 % 21.27/3.64 (m__1837) % 21.27/3.64 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 21.27/3.64 aNaturalNumber0(xn) % 21.27/3.64 % 21.27/3.64 (m__1870) % 21.27/3.64 $i(xp) & $i(xn) & ~ sdtlseqdt0(xp, xn) & ! [v0: $i] : ( ~ (sdtpldt0(xp, v0) % 21.27/3.64 = xn) | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 21.27/3.64 % 21.27/3.64 (m__2075) % 21.27/3.64 $i(xp) & $i(xm) & ~ sdtlseqdt0(xp, xm) & ! [v0: $i] : ( ~ (sdtpldt0(xp, v0) % 21.27/3.64 = xm) | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 21.27/3.64 % 21.27/3.64 (m__2287) % 21.27/3.64 $i(xp) & $i(xm) & $i(xn) & (xp = xm | xp = xn | ( ~ sdtlseqdt0(xm, xp) & ! % 21.27/3.64 [v0: $i] : ( ~ (sdtpldt0(xm, v0) = xp) | ~ $i(v0) | ~ % 21.27/3.64 aNaturalNumber0(v0))) | ( ~ sdtlseqdt0(xn, xp) & ! [v0: $i] : ( ~ % 21.27/3.64 (sdtpldt0(xn, v0) = xp) | ~ $i(v0) | ~ aNaturalNumber0(v0)))) % 21.27/3.64 % 21.27/3.64 Further assumptions not needed in the proof: % 21.27/3.64 -------------------------------------------- % 21.27/3.64 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefQuot, % 21.27/3.64 mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, % 21.27/3.64 mLERefl, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, mMulComm, % 21.27/3.64 mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero, % 21.27/3.64 m_MulUnit, m_MulZero, m__1799, m__1860 % 21.27/3.64 % 21.27/3.64 Those formulas are unsatisfiable: % 21.27/3.64 --------------------------------- % 21.27/3.64 % 21.27/3.64 Begin of proof % 21.51/3.64 | % 21.51/3.64 | ALPHA: (mSortsC_01) implies: % 21.51/3.64 | (1) aNaturalNumber0(sz10) % 21.51/3.64 | % 21.51/3.64 | ALPHA: (mLETotal) implies: % 21.51/3.64 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 21.51/3.64 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | % 21.51/3.64 | sdtlseqdt0(v0, v1)) % 21.51/3.64 | % 21.51/3.64 | ALPHA: (mDefPrime) implies: % 21.51/3.65 | (3) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 21.51/3.65 | % 21.51/3.65 | ALPHA: (m__1837) implies: % 21.52/3.65 | (4) aNaturalNumber0(xn) % 21.52/3.65 | (5) aNaturalNumber0(xm) % 21.52/3.65 | (6) aNaturalNumber0(xp) % 21.52/3.65 | % 21.52/3.65 | ALPHA: (m__1870) implies: % 21.52/3.65 | (7) ~ sdtlseqdt0(xp, xn) % 21.52/3.65 | % 21.52/3.65 | ALPHA: (m__2075) implies: % 21.52/3.65 | (8) ~ sdtlseqdt0(xp, xm) % 21.52/3.65 | % 21.52/3.65 | ALPHA: (m__2287) implies: % 21.52/3.65 | (9) xp = xm | xp = xn | ( ~ sdtlseqdt0(xm, xp) & ! [v0: $i] : ( ~ % 21.52/3.65 | (sdtpldt0(xm, v0) = xp) | ~ $i(v0) | ~ aNaturalNumber0(v0))) | ( % 21.52/3.65 | ~ sdtlseqdt0(xn, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xn, v0) = xp) | ~ % 21.52/3.65 | $i(v0) | ~ aNaturalNumber0(v0))) % 21.52/3.65 | % 21.52/3.65 | ALPHA: (m__) implies: % 21.52/3.65 | (10) $i(xn) % 21.52/3.65 | (11) $i(xm) % 21.52/3.65 | (12) $i(xp) % 21.52/3.65 | % 21.52/3.65 | BETA: splitting (3) gives: % 21.52/3.65 | % 21.52/3.65 | Case 1: % 21.52/3.65 | | % 21.52/3.65 | | (13) ~ aNaturalNumber0(sz10) % 21.52/3.65 | | % 21.52/3.65 | | PRED_UNIFY: (1), (13) imply: % 21.52/3.65 | | (14) $false % 21.52/3.65 | | % 21.52/3.65 | | CLOSE: (14) is inconsistent. % 21.52/3.65 | | % 21.52/3.65 | Case 2: % 21.52/3.65 | | % 21.52/3.65 | | % 21.52/3.65 | | GROUND_INST: instantiating (2) with xn, xn, simplifying with (4), (10) % 21.52/3.65 | | gives: % 21.52/3.65 | | (15) sdtlseqdt0(xn, xn) % 21.52/3.65 | | % 21.52/3.65 | | GROUND_INST: instantiating (2) with xm, xm, simplifying with (5), (11) % 21.52/3.65 | | gives: % 21.52/3.65 | | (16) sdtlseqdt0(xm, xm) % 21.52/3.65 | | % 21.52/3.65 | | GROUND_INST: instantiating (2) with xm, xp, simplifying with (5), (6), (8), % 21.52/3.65 | | (11), (12) gives: % 21.52/3.65 | | (17) sdtlseqdt0(xm, xp) % 21.52/3.65 | | % 21.52/3.65 | | GROUND_INST: instantiating (2) with xn, xp, simplifying with (4), (6), (7), % 21.52/3.65 | | (10), (12) gives: % 21.52/3.65 | | (18) sdtlseqdt0(xn, xp) % 21.52/3.65 | | % 21.52/3.65 | | PRED_UNIFY: (7), (15) imply: % 21.52/3.65 | | (19) ~ (xp = xn) % 21.52/3.65 | | % 21.52/3.65 | | PRED_UNIFY: (8), (16) imply: % 21.52/3.65 | | (20) ~ (xp = xm) % 21.52/3.65 | | % 21.52/3.65 | | BETA: splitting (9) gives: % 21.52/3.65 | | % 21.52/3.65 | | Case 1: % 21.52/3.65 | | | % 21.52/3.65 | | | (21) xp = xm % 21.52/3.65 | | | % 21.52/3.65 | | | REDUCE: (20), (21) imply: % 21.52/3.65 | | | (22) $false % 21.52/3.65 | | | % 21.52/3.65 | | | CLOSE: (22) is inconsistent. % 21.52/3.65 | | | % 21.52/3.65 | | Case 2: % 21.52/3.65 | | | % 21.52/3.65 | | | (23) xp = xn | ( ~ sdtlseqdt0(xm, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xm, % 21.52/3.65 | | | v0) = xp) | ~ $i(v0) | ~ aNaturalNumber0(v0))) | ( ~ % 21.52/3.65 | | | sdtlseqdt0(xn, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xn, v0) = xp) | % 21.52/3.65 | | | ~ $i(v0) | ~ aNaturalNumber0(v0))) % 21.52/3.65 | | | % 21.52/3.65 | | | BETA: splitting (23) gives: % 21.52/3.65 | | | % 21.52/3.65 | | | Case 1: % 21.52/3.65 | | | | % 21.52/3.65 | | | | (24) xp = xn % 21.52/3.65 | | | | % 21.52/3.65 | | | | REDUCE: (19), (24) imply: % 21.52/3.65 | | | | (25) $false % 21.52/3.65 | | | | % 21.52/3.65 | | | | CLOSE: (25) is inconsistent. % 21.52/3.65 | | | | % 21.52/3.65 | | | Case 2: % 21.52/3.65 | | | | % 21.52/3.66 | | | | (26) ( ~ sdtlseqdt0(xm, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = % 21.52/3.66 | | | | xp) | ~ $i(v0) | ~ aNaturalNumber0(v0))) | ( ~ % 21.52/3.66 | | | | sdtlseqdt0(xn, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xn, v0) = xp) % 21.52/3.66 | | | | | ~ $i(v0) | ~ aNaturalNumber0(v0))) % 21.52/3.66 | | | | % 21.52/3.66 | | | | BETA: splitting (26) gives: % 21.52/3.66 | | | | % 21.52/3.66 | | | | Case 1: % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | (27) ~ sdtlseqdt0(xm, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = % 21.52/3.66 | | | | | xp) | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | ALPHA: (27) implies: % 21.52/3.66 | | | | | (28) ~ sdtlseqdt0(xm, xp) % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | PRED_UNIFY: (17), (28) imply: % 21.52/3.66 | | | | | (29) $false % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | CLOSE: (29) is inconsistent. % 21.52/3.66 | | | | | % 21.52/3.66 | | | | Case 2: % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | (30) ~ sdtlseqdt0(xn, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xn, v0) = % 21.52/3.66 | | | | | xp) | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | ALPHA: (30) implies: % 21.52/3.66 | | | | | (31) ~ sdtlseqdt0(xn, xp) % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | PRED_UNIFY: (18), (31) imply: % 21.52/3.66 | | | | | (32) $false % 21.52/3.66 | | | | | % 21.52/3.66 | | | | | CLOSE: (32) is inconsistent. % 21.52/3.66 | | | | | % 21.52/3.66 | | | | End of split % 21.52/3.66 | | | | % 21.52/3.66 | | | End of split % 21.52/3.66 | | | % 21.52/3.66 | | End of split % 21.52/3.66 | | % 21.52/3.66 | End of split % 21.52/3.66 | % 21.52/3.66 End of proof % 21.52/3.66 % SZS output end Proof for theBenchmark % 21.52/3.66 % 21.52/3.66 3059ms %------------------------------------------------------------------------------