%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 13:57:47 EDT 2023 % Result : Theorem 10.37s 2.17s % Output : Proof 14.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Aug 27 01:45:41 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 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 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 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 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 % 3.20/1.13 Prover 4: Preprocessing ... % 3.20/1.13 Prover 1: Preprocessing ... % 3.24/1.16 Prover 5: Preprocessing ... % 3.24/1.16 Prover 2: Preprocessing ... % 3.24/1.16 Prover 3: Preprocessing ... % 3.24/1.16 Prover 0: Preprocessing ... % 3.24/1.17 Prover 6: Preprocessing ... % 7.70/1.79 Prover 1: Constructing countermodel ... % 8.21/1.83 Prover 5: Proving ... % 8.21/1.83 Prover 3: Constructing countermodel ... % 8.27/1.84 Prover 6: Proving ... % 9.11/1.98 Prover 4: Constructing countermodel ... % 9.11/1.98 Prover 2: Proving ... % 9.11/1.99 Prover 0: Proving ... % 10.37/2.17 Prover 3: proved (1521ms) % 10.37/2.17 % 10.37/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.37/2.17 % 10.37/2.17 Prover 2: stopped % 10.37/2.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.37/2.17 Prover 5: stopped % 10.37/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.37/2.18 Prover 0: stopped % 10.37/2.18 Prover 6: stopped % 10.37/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.37/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.37/2.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.84/2.23 Prover 11: Preprocessing ... % 10.84/2.24 Prover 7: Preprocessing ... % 10.84/2.24 Prover 10: Preprocessing ... % 10.84/2.24 Prover 13: Preprocessing ... % 10.84/2.24 Prover 8: Preprocessing ... % 11.95/2.37 Prover 10: Constructing countermodel ... % 11.95/2.40 Prover 7: Constructing countermodel ... % 11.95/2.41 Prover 8: Warning: ignoring some quantifiers % 11.95/2.42 Prover 8: Constructing countermodel ... % 11.95/2.43 Prover 13: Warning: ignoring some quantifiers % 12.59/2.46 Prover 13: Constructing countermodel ... % 13.04/2.52 Prover 11: Constructing countermodel ... % 14.09/2.68 Prover 10: Found proof (size 12) % 14.09/2.68 Prover 10: proved (508ms) % 14.09/2.69 Prover 7: stopped % 14.09/2.69 Prover 13: stopped % 14.09/2.69 Prover 11: stopped % 14.09/2.69 Prover 8: stopped % 14.09/2.69 Prover 4: stopped % 14.09/2.69 Prover 1: stopped % 14.09/2.69 % 14.09/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.09/2.69 % 14.09/2.69 % SZS output start Proof for theBenchmark % 14.09/2.69 Assumptions after simplification: % 14.09/2.69 --------------------------------- % 14.09/2.69 % 14.09/2.69 (m__) % 14.54/2.72 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: % 14.54/2.72 $i] : ((sdtpldt0(xl, xn) = v1 & $i(v1) & ~ aElementOf0(v1, xJ)) | % 14.54/2.72 (sdtpldt0(xk, xm) = v0 & $i(v0) & ~ aElementOf0(v0, xI))) % 14.54/2.72 % 14.54/2.72 (m__870) % 14.54/2.72 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0: % 14.54/2.72 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | % 14.54/2.72 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) % 14.54/2.72 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 14.54/2.72 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 14.54/2.72 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.54/2.72 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | % 14.54/2.72 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] : % 14.54/2.72 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 14.54/2.72 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 14.54/2.72 % 14.54/2.72 (m__934) % 14.54/2.72 sdtpldt0(xk, xl) = xx & $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) & % 14.54/2.72 aElementOf0(xl, xJ) & aElementOf0(xk, xI) % 14.54/2.72 % 14.54/2.72 (m__967) % 14.68/2.72 sdtpldt0(xm, xn) = xy & $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI) & % 14.68/2.73 aElementOf0(xn, xJ) & aElementOf0(xm, xI) % 14.68/2.73 % 14.68/2.73 Further assumptions not needed in the proof: % 14.68/2.73 -------------------------------------------- % 14.68/2.73 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, % 14.68/2.73 mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, % 14.68/2.73 mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, % 14.68/2.73 m__901 % 14.68/2.73 % 14.68/2.73 Those formulas are unsatisfiable: % 14.68/2.73 --------------------------------- % 14.68/2.73 % 14.68/2.73 Begin of proof % 14.69/2.73 | % 14.69/2.73 | ALPHA: (m__870) implies: % 14.69/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 14.69/2.73 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, % 14.69/2.73 | xI) | aElementOf0(v2, xI)) % 14.69/2.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 14.69/2.73 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, % 14.69/2.73 | xJ) | aElementOf0(v2, xJ)) % 14.69/2.73 | % 14.69/2.73 | ALPHA: (m__934) implies: % 14.69/2.73 | (3) aElementOf0(xk, xI) % 14.69/2.73 | (4) aElementOf0(xl, xJ) % 14.69/2.73 | % 14.69/2.73 | ALPHA: (m__967) implies: % 14.69/2.73 | (5) aElementOf0(xm, xI) % 14.69/2.73 | (6) aElementOf0(xn, xJ) % 14.69/2.73 | % 14.69/2.73 | ALPHA: (m__) implies: % 14.69/2.73 | (7) $i(xk) % 14.69/2.73 | (8) $i(xl) % 14.69/2.73 | (9) $i(xm) % 14.69/2.73 | (10) $i(xn) % 14.69/2.73 | (11) ? [v0: $i] : ? [v1: $i] : ((sdtpldt0(xl, xn) = v1 & $i(v1) & ~ % 14.69/2.73 | aElementOf0(v1, xJ)) | (sdtpldt0(xk, xm) = v0 & $i(v0) & ~ % 14.69/2.73 | aElementOf0(v0, xI))) % 14.69/2.73 | % 14.69/2.73 | DELTA: instantiating (11) with fresh symbols all_23_0, all_23_1 gives: % 14.69/2.73 | (12) (sdtpldt0(xl, xn) = all_23_0 & $i(all_23_0) & ~ aElementOf0(all_23_0, % 14.69/2.73 | xJ)) | (sdtpldt0(xk, xm) = all_23_1 & $i(all_23_1) & ~ % 14.69/2.73 | aElementOf0(all_23_1, xI)) % 14.69/2.73 | % 14.69/2.73 | BETA: splitting (12) gives: % 14.69/2.73 | % 14.69/2.73 | Case 1: % 14.69/2.73 | | % 14.69/2.73 | | (13) sdtpldt0(xl, xn) = all_23_0 & $i(all_23_0) & ~ % 14.69/2.73 | | aElementOf0(all_23_0, xJ) % 14.69/2.73 | | % 14.69/2.73 | | ALPHA: (13) implies: % 14.69/2.74 | | (14) ~ aElementOf0(all_23_0, xJ) % 14.69/2.74 | | (15) sdtpldt0(xl, xn) = all_23_0 % 14.69/2.74 | | % 14.69/2.74 | | GROUND_INST: instantiating (2) with xl, xn, all_23_0, simplifying with (4), % 14.69/2.74 | | (6), (8), (10), (14), (15) gives: % 14.69/2.74 | | (16) $false % 14.69/2.74 | | % 14.69/2.74 | | CLOSE: (16) is inconsistent. % 14.69/2.74 | | % 14.69/2.74 | Case 2: % 14.69/2.74 | | % 14.69/2.74 | | (17) sdtpldt0(xk, xm) = all_23_1 & $i(all_23_1) & ~ % 14.69/2.74 | | aElementOf0(all_23_1, xI) % 14.69/2.74 | | % 14.69/2.74 | | ALPHA: (17) implies: % 14.69/2.74 | | (18) ~ aElementOf0(all_23_1, xI) % 14.69/2.74 | | (19) sdtpldt0(xk, xm) = all_23_1 % 14.69/2.74 | | % 14.69/2.74 | | GROUND_INST: instantiating (1) with xk, xm, all_23_1, simplifying with (3), % 14.69/2.74 | | (5), (7), (9), (18), (19) gives: % 14.69/2.74 | | (20) $false % 14.69/2.74 | | % 14.69/2.74 | | CLOSE: (20) is inconsistent. % 14.69/2.74 | | % 14.69/2.74 | End of split % 14.69/2.74 | % 14.69/2.74 End of proof % 14.69/2.74 % SZS output end Proof for theBenchmark % 14.69/2.74 % 14.69/2.74 2114ms %------------------------------------------------------------------------------