%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM557+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 : n007.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 11:48:36 EDT 2023 % Result : Theorem 10.79s 2.25s % Output : Proof 15.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM557+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n007.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 15:02:25 EDT 2023 % 0.12/0.34 % CPUTime : % 0.62/0.67 ________ _____ % 0.62/0.67 ___ __ \_________(_)________________________________ % 0.62/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.67 % 0.62/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.67 (2023-06-19) % 0.62/0.67 % 0.62/0.67 (c) Philipp Rümmer, 2009-2023 % 0.62/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.67 Amanda Stjerna. % 0.62/0.67 Free software under BSD-3-Clause. % 0.62/0.67 % 0.62/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.67 % 0.62/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.69 Running up to 7 provers in parallel. % 0.62/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.23/1.36 Prover 4: Preprocessing ... % 4.23/1.36 Prover 1: Preprocessing ... % 4.64/1.40 Prover 6: Preprocessing ... % 4.64/1.40 Prover 0: Preprocessing ... % 4.64/1.40 Prover 5: Preprocessing ... % 4.64/1.40 Prover 2: Preprocessing ... % 4.64/1.40 Prover 3: Preprocessing ... % 10.79/2.22 Prover 5: Constructing countermodel ... % 10.79/2.25 Prover 5: proved (1547ms) % 10.79/2.25 % 10.79/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.79/2.25 % 10.79/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.53/2.32 Prover 3: Constructing countermodel ... % 11.53/2.34 Prover 3: stopped % 11.53/2.35 Prover 1: Constructing countermodel ... % 11.53/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.53/2.38 Prover 7: Preprocessing ... % 12.21/2.42 Prover 6: Proving ... % 12.21/2.43 Prover 6: stopped % 12.21/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.21/2.46 Prover 2: Proving ... % 12.21/2.46 Prover 8: Preprocessing ... % 12.21/2.46 Prover 2: stopped % 12.21/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.94/2.53 Prover 10: Preprocessing ... % 13.81/2.62 Prover 7: Constructing countermodel ... % 13.81/2.62 Prover 11: Preprocessing ... % 13.81/2.68 Prover 1: Found proof (size 13) % 13.81/2.69 Prover 1: proved (1989ms) % 13.81/2.69 Prover 7: stopped % 14.54/2.76 Prover 10: Constructing countermodel ... % 14.54/2.77 Prover 11: stopped % 14.54/2.77 Prover 4: Constructing countermodel ... % 14.54/2.78 Prover 8: Warning: ignoring some quantifiers % 15.12/2.79 Prover 10: stopped % 15.12/2.80 Prover 8: Constructing countermodel ... % 15.12/2.81 Prover 4: stopped % 15.12/2.81 Prover 8: stopped % 15.12/2.85 Prover 0: Proving ... % 15.12/2.85 Prover 0: stopped % 15.12/2.85 % 15.12/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.12/2.85 % 15.12/2.85 % SZS output start Proof for theBenchmark % 15.12/2.86 Assumptions after simplification: % 15.12/2.86 --------------------------------- % 15.12/2.86 % 15.12/2.86 (m__) % 15.56/2.88 $i(xP) & $i(xS) & $i(xk) & ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 15.56/2.88 int] : ( ~ (v3 = 0) & slbdtsldtrb0(xS, xk) = v2 & sbrdtbr0(xP) = v1 & % 15.56/2.88 aSubsetOf0(xP, xS) = v0 & aElementOf0(xP, v2) = v3 & $i(v2) & $i(v1) & ( ~ % 15.56/2.88 (v1 = xk) | ( ~ (v0 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 15.56/2.88 aElementOf0(v4, xP) = 0 & aElementOf0(v4, xS) = v5 & $i(v4))))) % 15.56/2.88 % 15.56/2.88 (m__2431) % 15.57/2.88 sbrdtbr0(xP) = xk & aSubsetOf0(xP, xS) = 0 & $i(xP) & $i(xS) & $i(xk) & ! % 15.57/2.88 [v0: $i] : ( ~ (aElementOf0(v0, xP) = 0) | ~ $i(v0) | aElementOf0(v0, xS) = % 15.57/2.88 0) % 15.57/2.88 % 15.57/2.88 (function-axioms) % 15.57/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.57/2.89 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: % 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.57/2.89 : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.57/2.89 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 15.57/2.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.57/2.89 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 15.57/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 15.57/2.89 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.57/2.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.57/2.89 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.57/2.89 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 15.57/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | % 15.57/2.89 ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.57/2.89 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! % 15.57/2.89 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ % 15.57/2.89 (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.57/2.89 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: % 15.57/2.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 15.57/2.89 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | % 15.57/2.89 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 15.57/2.89 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 15.57/2.89 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 15.57/2.89 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 15.57/2.89 % 15.57/2.89 Further assumptions not needed in the proof: % 15.57/2.89 -------------------------------------------- % 15.57/2.89 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 15.57/2.89 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 15.57/2.89 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub, % 15.57/2.89 mDiffCons, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, % 15.57/2.89 mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 15.57/2.89 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 15.57/2.89 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, % 15.57/2.89 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 15.57/2.89 mZeroLess, mZeroNum, m__2202, m__2202_02, m__2227, m__2256, m__2270, m__2291, % 15.57/2.89 m__2304, m__2323, m__2338, m__2357, m__2411 % 15.57/2.89 % 15.57/2.89 Those formulas are unsatisfiable: % 15.57/2.89 --------------------------------- % 15.57/2.89 % 15.57/2.89 Begin of proof % 15.57/2.90 | % 15.57/2.90 | ALPHA: (m__2431) implies: % 15.57/2.90 | (1) aSubsetOf0(xP, xS) = 0 % 15.57/2.90 | (2) sbrdtbr0(xP) = xk % 15.57/2.90 | % 15.57/2.90 | ALPHA: (m__) implies: % 15.65/2.90 | (3) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 15.65/2.90 | & slbdtsldtrb0(xS, xk) = v2 & sbrdtbr0(xP) = v1 & aSubsetOf0(xP, xS) % 15.65/2.90 | = v0 & aElementOf0(xP, v2) = v3 & $i(v2) & $i(v1) & ( ~ (v1 = xk) | ( % 15.65/2.90 | ~ (v0 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 15.65/2.90 | aElementOf0(v4, xP) = 0 & aElementOf0(v4, xS) = v5 & $i(v4))))) % 15.65/2.90 | % 15.65/2.90 | ALPHA: (function-axioms) implies: % 15.65/2.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = % 15.65/2.90 | v1) | ~ (sbrdtbr0(v2) = v0)) % 15.65/2.90 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.65/2.90 | ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 15.65/2.90 | (aSubsetOf0(v3, v2) = v0)) % 15.65/2.90 | % 15.65/2.90 | DELTA: instantiating (3) with fresh symbols all_61_0, all_61_1, all_61_2, % 15.65/2.90 | all_61_3 gives: % 15.65/2.90 | (6) ~ (all_61_0 = 0) & slbdtsldtrb0(xS, xk) = all_61_1 & sbrdtbr0(xP) = % 15.65/2.90 | all_61_2 & aSubsetOf0(xP, xS) = all_61_3 & aElementOf0(xP, all_61_1) = % 15.65/2.90 | all_61_0 & $i(all_61_1) & $i(all_61_2) & ( ~ (all_61_2 = xk) | ( ~ % 15.65/2.90 | (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.65/2.90 | aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)))) % 15.65/2.90 | % 15.65/2.90 | ALPHA: (6) implies: % 15.65/2.90 | (7) aSubsetOf0(xP, xS) = all_61_3 % 15.65/2.90 | (8) sbrdtbr0(xP) = all_61_2 % 15.65/2.90 | (9) ~ (all_61_2 = xk) | ( ~ (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] : % 15.65/2.91 | ( ~ (v1 = 0) & aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 & % 15.65/2.91 | $i(v0))) % 15.65/2.91 | % 15.65/2.91 | GROUND_INST: instantiating (5) with 0, all_61_3, xS, xP, simplifying with (1), % 15.65/2.91 | (7) gives: % 15.65/2.91 | (10) all_61_3 = 0 % 15.65/2.91 | % 15.65/2.91 | GROUND_INST: instantiating (4) with xk, all_61_2, xP, simplifying with (2), % 15.65/2.91 | (8) gives: % 15.65/2.91 | (11) all_61_2 = xk % 15.65/2.91 | % 15.65/2.91 | BETA: splitting (9) gives: % 15.65/2.91 | % 15.65/2.91 | Case 1: % 15.65/2.91 | | % 15.65/2.91 | | (12) ~ (all_61_2 = xk) % 15.65/2.91 | | % 15.65/2.91 | | REDUCE: (11), (12) imply: % 15.65/2.91 | | (13) $false % 15.65/2.91 | | % 15.65/2.91 | | CLOSE: (13) is inconsistent. % 15.65/2.91 | | % 15.65/2.91 | Case 2: % 15.65/2.91 | | % 15.65/2.91 | | (14) ~ (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.65/2.91 | | aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) % 15.65/2.91 | | % 15.65/2.91 | | ALPHA: (14) implies: % 15.65/2.91 | | (15) ~ (all_61_3 = 0) % 15.65/2.91 | | % 15.65/2.91 | | REDUCE: (10), (15) imply: % 15.65/2.91 | | (16) $false % 15.65/2.91 | | % 15.65/2.91 | | CLOSE: (16) is inconsistent. % 15.65/2.91 | | % 15.65/2.91 | End of split % 15.65/2.91 | % 15.65/2.91 End of proof % 15.65/2.91 % SZS output end Proof for theBenchmark % 15.65/2.91 % 15.65/2.91 2239ms %------------------------------------------------------------------------------