%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM505+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 : n015.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 11:48:14 EDT 2023 % Result : Theorem 14.45s 2.86s % Output : Proof 21.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM505+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n015.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 16:29:07 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.75/1.36 Prover 1: Preprocessing ... % 3.75/1.36 Prover 4: Preprocessing ... % 3.75/1.42 Prover 0: Preprocessing ... % 3.75/1.42 Prover 3: Preprocessing ... % 3.75/1.42 Prover 6: Preprocessing ... % 3.75/1.42 Prover 2: Preprocessing ... % 3.75/1.42 Prover 5: Preprocessing ... % 11.58/2.40 Prover 1: Constructing countermodel ... % 11.58/2.40 Prover 6: Proving ... % 11.58/2.43 Prover 3: Constructing countermodel ... % 12.12/2.48 Prover 5: Constructing countermodel ... % 13.52/2.72 Prover 2: Proving ... % 13.52/2.81 Prover 4: Constructing countermodel ... % 14.45/2.86 Prover 3: proved (2216ms) % 14.45/2.86 % 14.45/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.45/2.86 % 14.45/2.86 Prover 5: stopped % 15.04/2.87 Prover 6: stopped % 15.04/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.04/2.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.04/2.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.20/2.92 Prover 0: Proving ... % 15.47/2.93 Prover 0: stopped % 15.47/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.47/2.94 Prover 2: stopped % 15.47/2.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.47/2.94 Prover 8: Preprocessing ... % 15.47/2.95 Prover 7: Preprocessing ... % 15.99/3.04 Prover 10: Preprocessing ... % 16.48/3.07 Prover 11: Preprocessing ... % 16.48/3.13 Prover 13: Preprocessing ... % 17.48/3.22 Prover 8: Warning: ignoring some quantifiers % 17.51/3.24 Prover 8: Constructing countermodel ... % 17.51/3.28 Prover 10: Constructing countermodel ... % 17.51/3.32 Prover 7: Constructing countermodel ... % 19.65/3.55 Prover 13: Constructing countermodel ... % 20.32/3.67 Prover 11: Constructing countermodel ... % 20.74/3.70 Prover 10: Found proof (size 16) % 20.74/3.70 Prover 10: proved (817ms) % 20.74/3.70 Prover 4: stopped % 20.74/3.70 Prover 7: stopped % 20.74/3.70 Prover 13: stopped % 20.74/3.70 Prover 1: stopped % 20.74/3.70 Prover 11: stopped % 20.74/3.71 Prover 8: stopped % 20.74/3.71 % 20.74/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.74/3.71 % 20.74/3.71 % SZS output start Proof for theBenchmark % 20.74/3.71 Assumptions after simplification: % 20.74/3.71 --------------------------------- % 20.74/3.71 % 20.74/3.72 (mLETotal) % 20.74/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 20.74/3.72 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 20.74/3.72 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 20.74/3.72 % 20.74/3.72 (m__) % 20.74/3.74 $i(xk) & $i(xp) & ~ sdtlseqdt0(xp, xk) & ! [v0: $i] : ( ~ (sdtpldt0(xp, v0) % 20.74/3.74 = xk) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & (xk = xp | ( ~ % 20.74/3.74 sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0) = xp) | ~ $i(v0) % 20.74/3.74 | ~ aNaturalNumber0(v0)))) % 20.74/3.74 % 20.74/3.74 (m__1837) % 20.74/3.74 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 20.74/3.74 aNaturalNumber0(xn) % 20.74/3.74 % 20.74/3.74 (m__2306) % 20.74/3.75 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk & % 20.74/3.75 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) & % 20.74/3.75 aNaturalNumber0(xk)) % 20.74/3.75 % 20.74/3.75 Further assumptions not needed in the proof: % 20.74/3.75 -------------------------------------------- % 20.74/3.75 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime, % 20.74/3.75 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 20.74/3.75 mLENTr, mLERefl, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, % 20.74/3.75 mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, mSortsC_01, % 20.74/3.75 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, m__1860, m__1870, % 20.74/3.75 m__2075, m__2287, m__2315, m__2327, m__2342, m__2362 % 20.74/3.75 % 20.74/3.75 Those formulas are unsatisfiable: % 20.74/3.75 --------------------------------- % 20.74/3.75 % 20.74/3.75 Begin of proof % 20.74/3.75 | % 20.74/3.75 | ALPHA: (mLETotal) implies: % 20.74/3.75 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 20.74/3.75 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | % 20.74/3.75 | sdtlseqdt0(v0, v1)) % 20.74/3.75 | % 20.74/3.75 | ALPHA: (m__1837) implies: % 20.74/3.75 | (2) aNaturalNumber0(xp) % 20.74/3.75 | % 20.74/3.75 | ALPHA: (m__2306) implies: % 20.74/3.75 | (3) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 & % 20.74/3.75 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk)) % 20.74/3.75 | % 20.74/3.75 | ALPHA: (m__) implies: % 20.74/3.75 | (4) ~ sdtlseqdt0(xp, xk) % 20.74/3.75 | (5) $i(xp) % 20.74/3.75 | (6) $i(xk) % 20.74/3.75 | (7) xk = xp | ( ~ sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0) % 20.74/3.75 | = xp) | ~ $i(v0) | ~ aNaturalNumber0(v0))) % 20.74/3.75 | % 20.74/3.75 | DELTA: instantiating (3) with fresh symbol all_41_0 gives: % 20.74/3.75 | (8) sdtsldt0(all_41_0, xp) = xk & sdtasdt0(xp, xk) = all_41_0 & % 20.74/3.75 | sdtasdt0(xn, xm) = all_41_0 & $i(all_41_0) & aNaturalNumber0(xk) % 20.74/3.75 | % 20.74/3.75 | ALPHA: (8) implies: % 20.74/3.75 | (9) aNaturalNumber0(xk) % 20.74/3.75 | % 21.11/3.76 | GROUND_INST: instantiating (1) with xp, xk, simplifying with (2), (4), (5), % 21.11/3.76 | (6), (9) gives: % 21.11/3.76 | (10) sdtlseqdt0(xk, xp) % 21.11/3.76 | % 21.11/3.76 | BETA: splitting (7) gives: % 21.11/3.76 | % 21.11/3.76 | Case 1: % 21.11/3.76 | | % 21.11/3.76 | | (11) xk = xp % 21.11/3.76 | | % 21.11/3.76 | | REDUCE: (10), (11) imply: % 21.11/3.76 | | (12) sdtlseqdt0(xp, xp) % 21.11/3.76 | | % 21.11/3.76 | | REDUCE: (4), (11) imply: % 21.11/3.76 | | (13) ~ sdtlseqdt0(xp, xp) % 21.11/3.76 | | % 21.11/3.76 | | PRED_UNIFY: (12), (13) imply: % 21.11/3.76 | | (14) $false % 21.11/3.76 | | % 21.11/3.76 | | CLOSE: (14) is inconsistent. % 21.11/3.76 | | % 21.11/3.76 | Case 2: % 21.11/3.76 | | % 21.11/3.76 | | (15) ~ sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0) = xp) | % 21.11/3.76 | | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 21.11/3.76 | | % 21.11/3.76 | | ALPHA: (15) implies: % 21.11/3.76 | | (16) ~ sdtlseqdt0(xk, xp) % 21.11/3.76 | | % 21.11/3.76 | | PRED_UNIFY: (10), (16) imply: % 21.11/3.76 | | (17) $false % 21.11/3.76 | | % 21.11/3.76 | | CLOSE: (17) is inconsistent. % 21.11/3.76 | | % 21.11/3.76 | End of split % 21.11/3.76 | % 21.11/3.76 End of proof % 21.11/3.76 % SZS output end Proof for theBenchmark % 21.11/3.76 % 21.11/3.76 3143ms %------------------------------------------------------------------------------