%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG124+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 : n029.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 13:58:01 EDT 2023 % Result : Theorem 14.01s 2.72s % Output : Proof 18.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG124+1 : 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 : n029.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 : Sun Aug 27 03:16:10 EDT 2023 % 0.13/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.31/1.19 Prover 4: Preprocessing ... % 3.31/1.19 Prover 1: Preprocessing ... % 3.87/1.23 Prover 0: Preprocessing ... % 3.87/1.23 Prover 5: Preprocessing ... % 3.87/1.23 Prover 3: Preprocessing ... % 3.87/1.23 Prover 6: Preprocessing ... % 3.87/1.23 Prover 2: Preprocessing ... % 9.23/2.08 Prover 1: Constructing countermodel ... % 9.23/2.13 Prover 6: Proving ... % 9.23/2.15 Prover 5: Proving ... % 9.23/2.15 Prover 3: Constructing countermodel ... % 11.70/2.32 Prover 2: Proving ... % 11.99/2.38 Prover 4: Constructing countermodel ... % 13.18/2.49 Prover 0: Proving ... % 14.01/2.71 Prover 3: proved (2070ms) % 14.01/2.72 % 14.01/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.01/2.72 % 14.01/2.72 Prover 5: stopped % 14.01/2.72 Prover 2: stopped % 14.01/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.01/2.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.01/2.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.01/2.72 Prover 6: stopped % 14.01/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.01/2.72 Prover 0: stopped % 14.01/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.83/2.82 Prover 10: Preprocessing ... % 14.83/2.82 Prover 7: Preprocessing ... % 15.73/2.85 Prover 8: Preprocessing ... % 15.73/2.86 Prover 13: Preprocessing ... % 15.73/2.87 Prover 11: Preprocessing ... % 17.23/3.05 Prover 10: Constructing countermodel ... % 17.23/3.07 Prover 7: Constructing countermodel ... % 17.53/3.12 Prover 8: Warning: ignoring some quantifiers % 17.88/3.14 Prover 8: Constructing countermodel ... % 18.38/3.23 Prover 13: Warning: ignoring some quantifiers % 18.38/3.24 Prover 10: Found proof (size 18) % 18.38/3.24 Prover 10: proved (524ms) % 18.38/3.24 Prover 4: stopped % 18.38/3.24 Prover 8: stopped % 18.38/3.24 Prover 7: stopped % 18.38/3.24 Prover 1: stopped % 18.38/3.24 Prover 13: Constructing countermodel ... % 18.75/3.26 Prover 13: stopped % 18.75/3.26 Prover 11: Constructing countermodel ... % 18.75/3.27 Prover 11: stopped % 18.75/3.27 % 18.75/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.75/3.28 % 18.75/3.28 % SZS output start Proof for theBenchmark % 18.75/3.28 Assumptions after simplification: % 18.75/3.28 --------------------------------- % 18.75/3.28 % 18.75/3.28 (m__2273) % 18.75/3.30 $i(xu) & $i(xI) & $i(sz00) & ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 % 18.75/3.30 & $i(v0) & aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 18.75/3.30 (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~ aElementOf0(v1, % 18.75/3.30 xI))) % 18.75/3.30 % 18.75/3.30 (m__2666) % 18.75/3.31 $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 18.75/3.31 [v2: $i] : (sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb & $i(v0) & % 18.75/3.31 aElement0(xr) & aElement0(xq) & (xr = sz00 | (sbrdtbr0(xr) = v1 & % 18.75/3.31 sbrdtbr0(xu) = v2 & $i(v2) & $i(v1) & iLess0(v1, v2)))) % 18.75/3.31 % 18.75/3.31 (m__2673) % 18.75/3.31 ~ (xr = sz00) & $i(xr) & $i(sz00) % 18.75/3.31 % 18.75/3.31 (m__2729) % 18.75/3.31 $i(xr) & $i(xI) & aElementOf0(xr, xI) % 18.75/3.31 % 18.75/3.31 (function-axioms) % 18.75/3.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.75/3.31 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.75/3.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 18.75/3.31 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.75/3.31 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.75/3.31 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.75/3.31 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.75/3.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 18.75/3.31 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.75/3.31 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 18.75/3.31 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 18.75/3.31 % 18.75/3.31 Further assumptions not needed in the proof: % 18.75/3.31 -------------------------------------------- % 18.75/3.31 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 18.75/3.31 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, % 18.75/3.31 mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, % 18.75/3.31 mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, % 18.75/3.31 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__, % 18.75/3.31 m__2091, m__2110, m__2129, m__2174, m__2203, m__2228, m__2383, m__2416, m__2479, % 18.75/3.31 m__2612, m__2690, m__2699, m__2718 % 18.75/3.31 % 18.75/3.31 Those formulas are unsatisfiable: % 18.75/3.31 --------------------------------- % 18.75/3.31 % 18.75/3.31 Begin of proof % 18.75/3.31 | % 18.75/3.31 | ALPHA: (m__2273) implies: % 18.75/3.31 | (1) ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & $i(v0) & % 18.75/3.31 | aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 18.75/3.31 | (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~ % 18.75/3.31 | aElementOf0(v1, xI))) % 18.75/3.31 | % 18.75/3.31 | ALPHA: (m__2666) implies: % 18.75/3.31 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xq, xu) = v0 & % 18.75/3.31 | sdtpldt0(v0, xr) = xb & $i(v0) & aElement0(xr) & aElement0(xq) & (xr % 18.75/3.31 | = sz00 | (sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & $i(v2) & $i(v1) & % 18.75/3.31 | iLess0(v1, v2)))) % 18.75/3.31 | % 18.75/3.31 | ALPHA: (m__2673) implies: % 18.75/3.31 | (3) ~ (xr = sz00) % 18.75/3.31 | % 18.75/3.31 | ALPHA: (m__2729) implies: % 18.75/3.31 | (4) aElementOf0(xr, xI) % 18.75/3.32 | (5) $i(xr) % 18.75/3.32 | % 18.75/3.32 | ALPHA: (function-axioms) implies: % 18.75/3.32 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = % 18.75/3.32 | v1) | ~ (sbrdtbr0(v2) = v0)) % 18.75/3.32 | % 18.75/3.32 | DELTA: instantiating (1) with fresh symbol all_45_0 gives: % 18.75/3.32 | (7) ~ (xu = sz00) & sbrdtbr0(xu) = all_45_0 & $i(all_45_0) & % 18.75/3.32 | aElementOf0(xu, xI) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ % 18.75/3.32 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, all_45_0) | ~ % 18.75/3.32 | aElementOf0(v0, xI)) % 18.75/3.32 | % 18.75/3.32 | ALPHA: (7) implies: % 18.75/3.32 | (8) sbrdtbr0(xu) = all_45_0 % 18.75/3.32 | (9) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ % 18.75/3.32 | $i(v0) | ~ iLess0(v1, all_45_0) | ~ aElementOf0(v0, xI)) % 18.75/3.32 | % 18.75/3.32 | DELTA: instantiating (2) with fresh symbols all_52_0, all_52_1, all_52_2 % 18.75/3.32 | gives: % 18.75/3.32 | (10) sdtasdt0(xq, xu) = all_52_2 & sdtpldt0(all_52_2, xr) = xb & % 18.75/3.32 | $i(all_52_2) & aElement0(xr) & aElement0(xq) & (xr = sz00 | % 18.75/3.32 | (sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 & $i(all_52_0) & % 18.75/3.32 | $i(all_52_1) & iLess0(all_52_1, all_52_0))) % 18.75/3.32 | % 18.75/3.32 | ALPHA: (10) implies: % 18.75/3.32 | (11) xr = sz00 | (sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 & % 18.75/3.32 | $i(all_52_0) & $i(all_52_1) & iLess0(all_52_1, all_52_0)) % 18.75/3.32 | % 18.75/3.32 | BETA: splitting (11) gives: % 18.75/3.32 | % 18.75/3.32 | Case 1: % 18.75/3.32 | | % 18.75/3.32 | | (12) xr = sz00 % 18.75/3.32 | | % 18.75/3.32 | | REDUCE: (3), (12) imply: % 18.75/3.32 | | (13) $false % 18.75/3.32 | | % 18.75/3.32 | | CLOSE: (13) is inconsistent. % 18.75/3.32 | | % 18.75/3.32 | Case 2: % 18.75/3.32 | | % 18.75/3.32 | | (14) sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 & $i(all_52_0) & % 18.75/3.32 | | $i(all_52_1) & iLess0(all_52_1, all_52_0) % 18.75/3.32 | | % 18.75/3.32 | | ALPHA: (14) implies: % 18.75/3.32 | | (15) iLess0(all_52_1, all_52_0) % 18.75/3.32 | | (16) sbrdtbr0(xu) = all_52_0 % 18.75/3.32 | | (17) sbrdtbr0(xr) = all_52_1 % 18.75/3.32 | | % 18.75/3.32 | | GROUND_INST: instantiating (6) with all_45_0, all_52_0, xu, simplifying with % 18.75/3.32 | | (8), (16) gives: % 18.75/3.32 | | (18) all_52_0 = all_45_0 % 18.75/3.32 | | % 18.75/3.32 | | REDUCE: (15), (18) imply: % 18.75/3.32 | | (19) iLess0(all_52_1, all_45_0) % 18.75/3.32 | | % 18.75/3.32 | | GROUND_INST: instantiating (9) with xr, all_52_1, simplifying with (4), (5), % 18.75/3.32 | | (17), (19) gives: % 18.75/3.32 | | (20) xr = sz00 % 18.75/3.32 | | % 18.75/3.32 | | REDUCE: (3), (20) imply: % 18.75/3.32 | | (21) $false % 18.75/3.32 | | % 18.75/3.32 | | CLOSE: (21) is inconsistent. % 18.75/3.32 | | % 18.75/3.32 | End of split % 18.75/3.32 | % 18.75/3.32 End of proof % 18.75/3.32 % SZS output end Proof for theBenchmark % 18.75/3.32 % 18.75/3.32 2703ms %------------------------------------------------------------------------------