%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM594+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 : n014.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 11:48:50 EDT 2023 % Result : Theorem 23.45s 4.02s % Output : Proof 47.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : NUM594+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n014.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Aug 25 16:12:03 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.03/1.68 Prover 1: Preprocessing ... % 6.03/1.68 Prover 4: Preprocessing ... % 6.57/1.73 Prover 0: Preprocessing ... % 6.57/1.73 Prover 6: Preprocessing ... % 6.57/1.73 Prover 2: Preprocessing ... % 6.57/1.73 Prover 5: Preprocessing ... % 6.57/1.73 Prover 3: Preprocessing ... % 17.95/3.26 Prover 3: Constructing countermodel ... % 17.95/3.26 Prover 1: Constructing countermodel ... % 18.23/3.29 Prover 6: Proving ... % 20.25/3.73 Prover 5: Proving ... % 23.45/4.02 Prover 3: proved (3357ms) % 23.45/4.02 % 23.45/4.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.45/4.02 % 23.45/4.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.45/4.04 Prover 5: stopped % 23.45/4.05 Prover 6: stopped % 23.45/4.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.45/4.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.09/4.29 Prover 7: Preprocessing ... % 25.09/4.29 Prover 10: Preprocessing ... % 25.09/4.41 Prover 8: Preprocessing ... % 30.75/5.01 Prover 8: Warning: ignoring some quantifiers % 30.75/5.04 Prover 8: Constructing countermodel ... % 35.21/5.54 Prover 10: Constructing countermodel ... % 36.17/5.70 Prover 7: Constructing countermodel ... % 38.80/6.02 Prover 10: Found proof (size 16) % 38.80/6.02 Prover 10: proved (1963ms) % 38.80/6.02 Prover 7: stopped % 38.80/6.03 Prover 1: stopped % 38.80/6.03 Prover 8: stopped % 44.99/7.04 Prover 4: Constructing countermodel ... % 44.99/7.08 Prover 4: stopped % 47.27/7.48 Prover 2: Proving ... % 47.27/7.51 Prover 2: stopped % 47.27/7.52 Prover 0: Proving ... % 47.72/7.54 Prover 0: stopped % 47.72/7.55 % 47.72/7.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 47.72/7.55 % 47.72/7.55 % SZS output start Proof for theBenchmark % 47.72/7.55 Assumptions after simplification: % 47.72/7.55 --------------------------------- % 47.72/7.56 % 47.72/7.56 (m__) % 47.72/7.59 $i(xx) & $i(xd) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) | % 47.72/7.59 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)) % 47.72/7.59 % 47.94/7.59 (m__4730) % 47.94/7.60 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 47.94/7.60 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | % 47.94/7.60 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 47.94/7.60 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 47.94/7.60 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 47.94/7.60 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ % 47.94/7.61 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 47.94/7.61 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 47.94/7.61 ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ (sdtlpdtrp0(v5, v6) = v7) | ~ % 47.94/7.61 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 47.94/7.61 $i] : (v7 = v1 | ~ (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 47.94/7.61 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 47.94/7.61 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 47.94/7.61 % 47.94/7.61 (m__4769) % 47.94/7.61 $i(xd) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) % 47.94/7.61 = v0 & $i(v1) & $i(v0) & aSet0(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 47.94/7.61 (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, v0) % 47.94/7.61 | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) % 47.94/7.61 | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 47.94/7.61 % 47.94/7.61 (m__4781) % 47.94/7.61 $i(xx) & $i(xd) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlcdtrc0(xd, % 47.94/7.61 v0) = v1 & sdtlpdtrp0(xd, v2) = xx & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) % 47.94/7.61 & $i(v0) & aElementOf0(v2, v0) & aElementOf0(xx, v1)) % 47.94/7.61 % 47.94/7.61 (function-axioms) % 47.94/7.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.94/7.62 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 47.94/7.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 47.94/7.62 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 47.94/7.62 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 47.94/7.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 47.94/7.62 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 47.94/7.62 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 47.94/7.62 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 47.94/7.62 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 47.94/7.62 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 47.94/7.62 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 47.94/7.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 47.94/7.62 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 47.94/7.62 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 47.94/7.62 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 47.94/7.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 47.94/7.62 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 47.94/7.62 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 47.94/7.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 47.94/7.62 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 47.94/7.62 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 47.94/7.62 v0)) % 47.94/7.62 % 47.94/7.62 Further assumptions not needed in the proof: % 47.94/7.62 -------------------------------------------- % 47.94/7.62 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 47.94/7.62 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 47.94/7.62 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 47.94/7.62 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 47.94/7.62 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 47.94/7.62 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 47.94/7.62 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 47.94/7.62 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 47.94/7.62 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 47.94/7.62 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 47.94/7.62 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 47.94/7.62 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660 % 47.94/7.62 % 47.94/7.62 Those formulas are unsatisfiable: % 47.94/7.62 --------------------------------- % 47.94/7.62 % 47.94/7.62 Begin of proof % 47.94/7.62 | % 47.94/7.62 | ALPHA: (m__4730) implies: % 47.94/7.63 | (1) szDzozmdt0(xd) = szNzAzT0 % 47.94/7.63 | % 47.94/7.63 | ALPHA: (m__4769) implies: % 47.94/7.63 | (2) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 47.94/7.63 | v0 & $i(v1) & $i(v0) & aSet0(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 47.94/7.63 | (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 47.94/7.63 | aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 47.94/7.63 | $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) % 47.94/7.63 | = v2 & $i(v3) & aElementOf0(v3, v0)))) % 47.94/7.63 | % 47.94/7.63 | ALPHA: (m__4781) implies: % 47.94/7.63 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 47.94/7.63 | sdtlpdtrp0(xd, v2) = xx & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & % 47.94/7.63 | $i(v0) & aElementOf0(v2, v0) & aElementOf0(xx, v1)) % 47.94/7.63 | % 47.94/7.63 | ALPHA: (m__) implies: % 47.94/7.63 | (4) ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) | ~ $i(v0) | ~ % 47.94/7.63 | aElementOf0(v0, szNzAzT0)) % 47.94/7.63 | % 47.94/7.63 | ALPHA: (function-axioms) implies: % 47.94/7.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzozmdt0(v2) % 47.94/7.63 | = v1) | ~ (szDzozmdt0(v2) = v0)) % 47.94/7.63 | % 47.94/7.63 | DELTA: instantiating (3) with fresh symbols all_78_0, all_78_1, all_78_2 % 47.94/7.63 | gives: % 47.94/7.63 | (6) sdtlcdtrc0(xd, all_78_2) = all_78_1 & sdtlpdtrp0(xd, all_78_0) = xx & % 47.94/7.63 | szDzozmdt0(xd) = all_78_2 & $i(all_78_0) & $i(all_78_1) & $i(all_78_2) % 47.94/7.63 | & aElementOf0(all_78_0, all_78_2) & aElementOf0(xx, all_78_1) % 47.94/7.63 | % 47.94/7.63 | ALPHA: (6) implies: % 47.94/7.63 | (7) aElementOf0(all_78_0, all_78_2) % 47.94/7.63 | (8) $i(all_78_0) % 47.94/7.63 | (9) szDzozmdt0(xd) = all_78_2 % 47.94/7.63 | (10) sdtlpdtrp0(xd, all_78_0) = xx % 47.94/7.63 | % 47.94/7.63 | DELTA: instantiating (2) with fresh symbols all_80_0, all_80_1 gives: % 47.94/7.63 | (11) sdtlcdtrc0(xd, all_80_1) = all_80_0 & szDzozmdt0(xd) = all_80_1 & % 47.94/7.63 | $i(all_80_0) & $i(all_80_1) & aSet0(all_80_0) & ! [v0: $i] : ! [v1: % 47.94/7.63 | $i] : ( ~ (sdtlpdtrp0(xd, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 47.94/7.63 | aElementOf0(v1, all_80_1) | aElementOf0(v0, all_80_0)) & ! [v0: $i] % 47.94/7.63 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_80_0) | ? [v1: $i] : % 47.94/7.63 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_80_1))) % 47.94/7.63 | % 47.94/7.63 | ALPHA: (11) implies: % 47.94/7.63 | (12) szDzozmdt0(xd) = all_80_1 % 47.94/7.63 | % 47.94/7.63 | GROUND_INST: instantiating (5) with all_78_2, all_80_1, xd, simplifying with % 47.94/7.63 | (9), (12) gives: % 47.94/7.63 | (13) all_80_1 = all_78_2 % 47.94/7.63 | % 47.94/7.63 | GROUND_INST: instantiating (5) with szNzAzT0, all_80_1, xd, simplifying with % 47.94/7.63 | (1), (12) gives: % 47.94/7.63 | (14) all_80_1 = szNzAzT0 % 47.94/7.63 | % 47.94/7.63 | COMBINE_EQS: (13), (14) imply: % 47.94/7.63 | (15) all_78_2 = szNzAzT0 % 47.94/7.63 | % 47.94/7.63 | REDUCE: (7), (15) imply: % 47.94/7.63 | (16) aElementOf0(all_78_0, szNzAzT0) % 47.94/7.64 | % 47.94/7.64 | GROUND_INST: instantiating (4) with all_78_0, simplifying with (8), (10), (16) % 47.94/7.64 | gives: % 47.94/7.64 | (17) $false % 47.94/7.64 | % 47.94/7.64 | CLOSE: (17) is inconsistent. % 47.94/7.64 | % 47.94/7.64 End of proof % 47.94/7.64 % SZS output end Proof for theBenchmark % 47.94/7.64 % 47.94/7.64 7005ms %------------------------------------------------------------------------------