%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG095+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 : 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 13:57:50 EDT 2023 % Result : Theorem 21.70s 3.70s % Output : Proof 22.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG095+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n015.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 : Sun Aug 27 02:37:38 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.85/1.10 Prover 4: Preprocessing ... % 2.85/1.10 Prover 1: Preprocessing ... % 2.85/1.14 Prover 6: Preprocessing ... % 2.85/1.14 Prover 3: Preprocessing ... % 2.85/1.14 Prover 0: Preprocessing ... % 2.85/1.14 Prover 2: Preprocessing ... % 2.85/1.14 Prover 5: Preprocessing ... % 7.00/1.72 Prover 1: Constructing countermodel ... % 7.63/1.76 Prover 3: Constructing countermodel ... % 7.63/1.78 Prover 6: Proving ... % 8.14/1.85 Prover 5: Proving ... % 8.14/1.85 Prover 2: Proving ... % 8.14/1.87 Prover 4: Constructing countermodel ... % 8.47/1.91 Prover 0: Proving ... % 15.35/2.78 Prover 3: gave up % 15.35/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.35/2.85 Prover 7: Preprocessing ... % 16.46/2.99 Prover 7: Constructing countermodel ... % 21.70/3.69 Prover 7: Found proof (size 17) % 21.70/3.70 Prover 7: proved (898ms) % 21.70/3.70 Prover 0: stopped % 21.70/3.70 Prover 6: stopped % 21.70/3.70 Prover 2: stopped % 21.70/3.70 Prover 1: stopped % 21.70/3.70 Prover 5: stopped % 21.70/3.70 Prover 4: stopped % 21.70/3.70 % 21.70/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.70/3.70 % 21.70/3.70 % SZS output start Proof for theBenchmark % 21.70/3.71 Assumptions after simplification: % 21.70/3.71 --------------------------------- % 21.70/3.71 % 21.70/3.71 (mDefIdeal) % 22.21/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 22.21/3.74 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 22.21/3.74 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 22.21/3.74 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 22.21/3.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 22.21/3.74 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 22.21/3.74 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 22.21/3.74 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 22.21/3.74 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 22.21/3.74 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 22.21/3.74 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 22.21/3.74 aElementOf0(v5, v0))))) % 22.21/3.74 % 22.21/3.74 (mDefSSum) % 22.21/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.21/3.74 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 22.21/3.74 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.21/3.74 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 22.21/3.74 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 22.21/3.74 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 22.21/3.75 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 22.21/3.75 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 22.21/3.75 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 22.21/3.75 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 22.21/3.75 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 22.21/3.75 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.21/3.75 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 22.21/3.75 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 22.21/3.75 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 22.21/3.75 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 22.21/3.75 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.21/3.75 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 22.21/3.75 % 22.21/3.75 (mSortsC_01) % 22.21/3.75 $i(sz10) & aElement0(sz10) % 22.21/3.75 % 22.21/3.75 (m__) % 22.21/3.75 $i(xJ) & $i(xI) & $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) % 22.21/3.75 = sz10) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ % 22.21/3.75 aElementOf0(v0, xI)) % 22.21/3.75 % 22.21/3.75 (m__1205) % 22.21/3.75 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) % 22.21/3.75 % 22.21/3.75 (m__1205_03) % 22.21/3.75 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] % 22.21/3.75 : ( ~ $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0))) % 22.21/3.75 % 22.21/3.75 Further assumptions not needed in the proof: % 22.21/3.75 -------------------------------------------- % 22.21/3.75 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefMod, mDefSInt, % 22.21/3.75 mEOfElem, mElmSort, mIdeInt, mIdeSum, mMulAsso, mMulComm, mMulMnOne, mMulUnit, % 22.21/3.75 mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsU, mUnNeZr, % 22.21/3.75 m__1217 % 22.21/3.75 % 22.21/3.75 Those formulas are unsatisfiable: % 22.21/3.75 --------------------------------- % 22.21/3.75 % 22.21/3.75 Begin of proof % 22.21/3.75 | % 22.21/3.75 | ALPHA: (mSortsC_01) implies: % 22.21/3.75 | (1) aElement0(sz10) % 22.21/3.75 | % 22.21/3.75 | ALPHA: (mDefSSum) implies: % 22.21/3.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 22.21/3.75 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 22.21/3.75 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? % 22.21/3.75 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 22.21/3.75 | aElementOf0(v5, v1) & aElementOf0(v4, v0))) % 22.21/3.75 | % 22.21/3.75 | ALPHA: (mDefIdeal) implies: % 22.21/3.75 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0)) % 22.21/3.75 | % 22.21/3.75 | ALPHA: (m__1205) implies: % 22.21/3.76 | (4) aIdeal0(xI) % 22.21/3.76 | (5) aIdeal0(xJ) % 22.21/3.76 | % 22.21/3.76 | ALPHA: (m__1205_03) implies: % 22.21/3.76 | (6) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 22.21/3.76 | $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0))) % 22.21/3.76 | % 22.21/3.76 | ALPHA: (m__) implies: % 22.21/3.76 | (7) $i(sz10) % 22.21/3.76 | (8) $i(xI) % 22.21/3.76 | (9) $i(xJ) % 22.21/3.76 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = sz10) | ~ $i(v1) % 22.21/3.76 | | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI)) % 22.21/3.76 | % 22.21/3.76 | DELTA: instantiating (6) with fresh symbol all_26_0 gives: % 22.21/3.76 | (11) sdtpldt1(xI, xJ) = all_26_0 & $i(all_26_0) & ! [v0: $i] : ( ~ $i(v0) % 22.21/3.76 | | ~ aElement0(v0) | aElementOf0(v0, all_26_0)) % 22.21/3.76 | % 22.21/3.76 | ALPHA: (11) implies: % 22.21/3.76 | (12) $i(all_26_0) % 22.21/3.76 | (13) sdtpldt1(xI, xJ) = all_26_0 % 22.21/3.76 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ aElement0(v0) | aElementOf0(v0, % 22.21/3.76 | all_26_0)) % 22.21/3.76 | % 22.21/3.76 | GROUND_INST: instantiating (14) with sz10, simplifying with (1), (7) gives: % 22.21/3.76 | (15) aElementOf0(sz10, all_26_0) % 22.21/3.76 | % 22.21/3.76 | GROUND_INST: instantiating (3) with xI, simplifying with (4), (8) gives: % 22.21/3.76 | (16) aSet0(xI) % 22.21/3.76 | % 22.21/3.76 | GROUND_INST: instantiating (3) with xJ, simplifying with (5), (9) gives: % 22.21/3.76 | (17) aSet0(xJ) % 22.21/3.76 | % 22.21/3.76 | GROUND_INST: instantiating (2) with xI, xJ, all_26_0, sz10, simplifying with % 22.21/3.76 | (7), (8), (9), (12), (13), (15), (16), (17) gives: % 22.21/3.76 | (18) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = sz10 & $i(v1) & $i(v0) % 22.21/3.76 | & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 22.21/3.76 | % 22.21/3.76 | DELTA: instantiating (18) with fresh symbols all_52_0, all_52_1 gives: % 22.21/3.76 | (19) sdtpldt0(all_52_1, all_52_0) = sz10 & $i(all_52_0) & $i(all_52_1) & % 22.21/3.76 | aElementOf0(all_52_0, xJ) & aElementOf0(all_52_1, xI) % 22.21/3.76 | % 22.21/3.76 | ALPHA: (19) implies: % 22.21/3.76 | (20) aElementOf0(all_52_1, xI) % 22.21/3.76 | (21) aElementOf0(all_52_0, xJ) % 22.21/3.76 | (22) $i(all_52_1) % 22.21/3.76 | (23) $i(all_52_0) % 22.21/3.76 | (24) sdtpldt0(all_52_1, all_52_0) = sz10 % 22.21/3.76 | % 22.21/3.76 | GROUND_INST: instantiating (10) with all_52_1, all_52_0, simplifying with % 22.21/3.76 | (20), (21), (22), (23), (24) gives: % 22.21/3.76 | (25) $false % 22.21/3.76 | % 22.21/3.76 | CLOSE: (25) is inconsistent. % 22.21/3.76 | % 22.21/3.76 End of proof % 22.21/3.77 % SZS output end Proof for theBenchmark % 22.21/3.77 % 22.21/3.77 3152ms %------------------------------------------------------------------------------