%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM560+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 : n016.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 11:48:37 EDT 2023 % Result : Theorem 13.69s 2.69s % Output : Proof 17.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM560+2 : 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 : n016.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 : Fri Aug 25 09:35:55 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.69/1.30 Prover 1: Preprocessing ... % 3.69/1.30 Prover 4: Preprocessing ... % 4.11/1.33 Prover 2: Preprocessing ... % 4.11/1.33 Prover 0: Preprocessing ... % 4.11/1.33 Prover 6: Preprocessing ... % 4.11/1.33 Prover 3: Preprocessing ... % 4.11/1.33 Prover 5: Preprocessing ... % 11.46/2.38 Prover 6: Proving ... % 11.46/2.38 Prover 3: Constructing countermodel ... % 11.46/2.38 Prover 1: Constructing countermodel ... % 11.46/2.40 Prover 5: Constructing countermodel ... % 13.16/2.59 Prover 2: Proving ... % 13.69/2.68 Prover 4: Constructing countermodel ... % 13.69/2.68 Prover 3: proved (2059ms) % 13.69/2.68 % 13.69/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.69/2.69 % 13.69/2.69 Prover 5: stopped % 13.69/2.71 Prover 6: stopped % 13.69/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.69/2.72 Prover 2: stopped % 14.40/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.40/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.40/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.89/2.82 Prover 8: Preprocessing ... % 14.89/2.84 Prover 7: Preprocessing ... % 14.89/2.88 Prover 10: Preprocessing ... % 14.89/2.88 Prover 1: Found proof (size 11) % 14.89/2.89 Prover 1: proved (2272ms) % 14.89/2.91 Prover 7: stopped % 14.89/2.91 Prover 11: Preprocessing ... % 14.89/2.93 Prover 0: Proving ... % 14.89/2.93 Prover 0: stopped % 14.89/2.95 Prover 4: stopped % 14.89/2.95 Prover 10: stopped % 16.40/3.02 Prover 11: stopped % 16.60/3.06 Prover 8: Warning: ignoring some quantifiers % 16.60/3.08 Prover 8: Constructing countermodel ... % 16.60/3.09 Prover 8: stopped % 16.60/3.09 % 16.60/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.60/3.09 % 16.60/3.09 % SZS output start Proof for theBenchmark % 16.60/3.10 Assumptions after simplification: % 16.60/3.10 --------------------------------- % 16.60/3.10 % 16.60/3.10 (m__) % 16.60/3.12 $i(xy) & $i(xF) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 16.60/3.12 sdtlbdtrb0(xF, xy) = v0 & szDzozmdt0(xF) = v1 & aSubsetOf0(v0, v1) = v2 & % 16.60/3.12 aSet0(v0) = 0 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 16.60/3.12 (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : % 16.60/3.12 (sdtlpdtrp0(xF, v3) = v6 & aElementOf0(v3, v1) = v5 & $i(v6) & ( ~ (v6 = % 16.60/3.12 xy) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v0) = 0) | % 16.60/3.12 ~ $i(v3) | (sdtlpdtrp0(xF, v3) = xy & aElementOf0(v3, v1) = 0)) & ? [v3: % 16.60/3.12 $i] : ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = v4 & % 16.60/3.12 aElementOf0(v3, v0) = 0 & $i(v3))) % 16.60/3.12 % 16.60/3.12 (function-axioms) % 16.60/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.60/3.13 (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.60/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlpdtrp0(v3, v2) = v1) % 16.60/3.13 | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.60/3.13 ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, % 16.60/3.13 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.60/3.13 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ % 16.60/3.13 (iLess0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.60/3.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.60/3.13 (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.60/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 16.60/3.13 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.60/3.13 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.60/3.13 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.60/3.13 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = % 16.60/3.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.60/3.13 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 16.60/3.13 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.60/3.13 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 16.60/3.13 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 16.60/3.13 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 16.60/3.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 16.60/3.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.60/3.13 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 16.60/3.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 16.60/3.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.60/3.13 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.60/3.13 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 17.05/3.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.05/3.13 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 17.05/3.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 17.05/3.13 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 17.05/3.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.05/3.13 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.05/3.13 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 17.05/3.13 ~ (aElement0(v2) = v0)) % 17.05/3.13 % 17.05/3.13 Further assumptions not needed in the proof: % 17.05/3.13 -------------------------------------------- % 17.05/3.13 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 17.05/3.13 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 17.05/3.13 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefSeg, mDefSel, % 17.05/3.13 mDefSub, mDiffCons, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, % 17.05/3.13 mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mLessASymm, mLessRefl, % 17.05/3.13 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, % 17.05/3.13 mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, % 17.05/3.13 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, % 17.05/3.13 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__2693 % 17.05/3.13 % 17.05/3.13 Those formulas are unsatisfiable: % 17.05/3.13 --------------------------------- % 17.05/3.13 % 17.05/3.13 Begin of proof % 17.05/3.13 | % 17.05/3.14 | ALPHA: (m__) implies: % 17.05/3.14 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 17.05/3.14 | sdtlbdtrb0(xF, xy) = v0 & szDzozmdt0(xF) = v1 & aSubsetOf0(v0, v1) = % 17.05/3.14 | v2 & aSet0(v0) = 0 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : % 17.05/3.14 | (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : % 17.05/3.14 | ? [v6: $i] : (sdtlpdtrp0(xF, v3) = v6 & aElementOf0(v3, v1) = v5 & % 17.05/3.14 | $i(v6) & ( ~ (v6 = xy) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~ % 17.05/3.14 | (aElementOf0(v3, v0) = 0) | ~ $i(v3) | (sdtlpdtrp0(xF, v3) = xy & % 17.05/3.14 | aElementOf0(v3, v1) = 0)) & ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 17.05/3.14 | = 0) & aElementOf0(v3, v1) = v4 & aElementOf0(v3, v0) = 0 & % 17.05/3.14 | $i(v3))) % 17.05/3.14 | % 17.05/3.14 | ALPHA: (function-axioms) implies: % 17.05/3.14 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.05/3.14 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 17.05/3.14 | (aElementOf0(v3, v2) = v0)) % 17.05/3.14 | % 17.05/3.14 | DELTA: instantiating (1) with fresh symbols all_58_0, all_58_1, all_58_2 % 17.05/3.14 | gives: % 17.05/3.14 | (3) ~ (all_58_0 = 0) & sdtlbdtrb0(xF, xy) = all_58_2 & szDzozmdt0(xF) = % 17.05/3.14 | all_58_1 & aSubsetOf0(all_58_2, all_58_1) = all_58_0 & aSet0(all_58_2) % 17.05/3.14 | = 0 & $i(all_58_1) & $i(all_58_2) & ! [v0: $i] : ! [v1: int] : (v1 = % 17.05/3.14 | 0 | ~ (aElementOf0(v0, all_58_2) = v1) | ~ $i(v0) | ? [v2: any] : % 17.05/3.14 | ? [v3: $i] : (sdtlpdtrp0(xF, v0) = v3 & aElementOf0(v0, all_58_1) = % 17.05/3.14 | v2 & $i(v3) & ( ~ (v3 = xy) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ % 17.05/3.14 | (aElementOf0(v0, all_58_2) = 0) | ~ $i(v0) | (sdtlpdtrp0(xF, v0) = % 17.05/3.14 | xy & aElementOf0(v0, all_58_1) = 0)) & ? [v0: $i] : ? [v1: int] : % 17.05/3.14 | ( ~ (v1 = 0) & aElementOf0(v0, all_58_1) = v1 & aElementOf0(v0, % 17.05/3.14 | all_58_2) = 0 & $i(v0)) % 17.05/3.14 | % 17.05/3.14 | ALPHA: (3) implies: % 17.05/3.14 | (4) ! [v0: $i] : ( ~ (aElementOf0(v0, all_58_2) = 0) | ~ $i(v0) | % 17.05/3.14 | (sdtlpdtrp0(xF, v0) = xy & aElementOf0(v0, all_58_1) = 0)) % 17.05/3.14 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, all_58_1) = % 17.05/3.14 | v1 & aElementOf0(v0, all_58_2) = 0 & $i(v0)) % 17.05/3.14 | % 17.05/3.14 | DELTA: instantiating (5) with fresh symbols all_61_0, all_61_1 gives: % 17.05/3.14 | (6) ~ (all_61_0 = 0) & aElementOf0(all_61_1, all_58_1) = all_61_0 & % 17.05/3.14 | aElementOf0(all_61_1, all_58_2) = 0 & $i(all_61_1) % 17.05/3.14 | % 17.05/3.14 | ALPHA: (6) implies: % 17.05/3.15 | (7) ~ (all_61_0 = 0) % 17.05/3.15 | (8) $i(all_61_1) % 17.05/3.15 | (9) aElementOf0(all_61_1, all_58_2) = 0 % 17.05/3.15 | (10) aElementOf0(all_61_1, all_58_1) = all_61_0 % 17.05/3.15 | % 17.05/3.15 | GROUND_INST: instantiating (4) with all_61_1, simplifying with (8), (9) gives: % 17.05/3.15 | (11) sdtlpdtrp0(xF, all_61_1) = xy & aElementOf0(all_61_1, all_58_1) = 0 % 17.05/3.15 | % 17.05/3.15 | ALPHA: (11) implies: % 17.05/3.15 | (12) aElementOf0(all_61_1, all_58_1) = 0 % 17.05/3.15 | % 17.05/3.15 | GROUND_INST: instantiating (2) with all_61_0, 0, all_58_1, all_61_1, % 17.05/3.15 | simplifying with (10), (12) gives: % 17.05/3.15 | (13) all_61_0 = 0 % 17.05/3.15 | % 17.05/3.15 | REDUCE: (7), (13) imply: % 17.05/3.15 | (14) $false % 17.05/3.15 | % 17.05/3.15 | CLOSE: (14) is inconsistent. % 17.05/3.15 | % 17.05/3.15 End of proof % 17.05/3.15 % SZS output end Proof for theBenchmark % 17.05/3.15 % 17.05/3.15 2544ms %------------------------------------------------------------------------------