%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM607+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 : n022.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 11:48:56 EDT 2023 % Result : Theorem 24.58s 4.07s % Output : Proof 42.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM607+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n022.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Fri Aug 25 14:57:40 EDT 2023 % 0.17/0.34 % CPUTime : % 0.21/0.64 ________ _____ % 0.21/0.64 ___ __ \_________(_)________________________________ % 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.64 % 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.64 (2023-06-19) % 0.21/0.64 % 0.21/0.64 (c) Philipp Rümmer, 2009-2023 % 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.64 Amanda Stjerna. % 0.21/0.64 Free software under BSD-3-Clause. % 0.21/0.64 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.66 Running up to 7 provers in parallel. % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.26/1.65 Prover 4: Preprocessing ... % 6.26/1.65 Prover 1: Preprocessing ... % 6.26/1.68 Prover 5: Preprocessing ... % 6.26/1.68 Prover 2: Preprocessing ... % 6.26/1.68 Prover 6: Preprocessing ... % 6.26/1.68 Prover 3: Preprocessing ... % 6.26/1.68 Prover 0: Preprocessing ... % 19.08/3.33 Prover 1: Constructing countermodel ... % 19.44/3.37 Prover 6: Proving ... % 19.44/3.44 Prover 3: Constructing countermodel ... % 21.57/3.72 Prover 5: Proving ... % 24.58/4.06 Prover 3: proved (3400ms) % 24.58/4.06 % 24.58/4.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.58/4.07 % 24.58/4.07 Prover 6: stopped % 24.58/4.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.58/4.07 Prover 5: stopped % 24.58/4.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.58/4.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.99/4.28 Prover 7: Preprocessing ... % 26.48/4.32 Prover 8: Preprocessing ... % 26.84/4.38 Prover 10: Preprocessing ... % 29.89/4.84 Prover 8: Warning: ignoring some quantifiers % 29.89/4.88 Prover 8: Constructing countermodel ... % 32.85/5.15 Prover 10: Constructing countermodel ... % 34.55/5.55 Prover 7: Constructing countermodel ... % 36.45/5.63 Prover 10: Found proof (size 15) % 36.45/5.63 Prover 10: proved (1550ms) % 36.45/5.63 Prover 7: stopped % 36.45/5.64 Prover 1: stopped % 36.45/5.64 Prover 8: stopped % 40.44/6.31 Prover 4: Constructing countermodel ... % 40.86/6.34 Prover 4: stopped % 41.12/6.42 Prover 2: Proving ... % 41.54/6.45 Prover 2: stopped % 42.52/6.70 Prover 0: Proving ... % 42.52/6.73 Prover 0: stopped % 42.52/6.73 % 42.52/6.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 42.52/6.73 % 42.52/6.74 % SZS output start Proof for theBenchmark % 42.84/6.75 Assumptions after simplification: % 42.84/6.75 --------------------------------- % 42.84/6.75 % 42.84/6.75 (mSubTrans) % 42.84/6.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 42.84/6.76 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) % 42.84/6.76 | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 42.84/6.76 % 42.84/6.76 (m__) % 42.84/6.81 $i(xQ) & $i(xc) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 42.84/6.81 (szDzozmdt0(xc) = v0 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, xQ) & % 42.84/6.81 aElementOf0(v1, xQ) & ~ aSubsetOf0(xQ, xS) & ~ aElementOf0(v2, xS) & ~ % 42.84/6.81 aElementOf0(v1, xS) & ~ aElementOf0(xQ, v0)) % 42.84/6.81 % 42.84/6.81 (m__3435) % 42.84/6.81 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) & % 42.84/6.81 aSet0(xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | % 42.84/6.81 aElementOf0(v0, szNzAzT0)) % 42.84/6.81 % 42.84/6.81 (m__4891) % 42.84/6.81 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 42.84/6.81 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 42.84/6.81 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 42.84/6.81 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 42.84/6.81 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 42.84/6.81 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 42.84/6.81 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 42.84/6.81 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 42.84/6.81 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 42.84/6.81 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 42.84/6.81 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 42.84/6.81 aElementOf0(v4, v1)))) % 42.84/6.82 % 42.84/6.82 (m__4998) % 42.84/6.82 $i(xO) & $i(xS) & aSubsetOf0(xO, xS) & ! [v0: $i] : ( ~ $i(v0) | ~ % 42.84/6.82 aElementOf0(v0, xO) | aElementOf0(v0, xS)) % 42.84/6.82 % 42.84/6.82 (m__5078) % 42.84/6.82 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 42.84/6.82 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 42.84/6.82 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 42.84/6.82 aElementOf0(v1, xO))) % 42.84/6.82 % 42.84/6.82 (m__5093) % 42.84/6.82 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & % 42.84/6.82 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 42.84/6.82 aElementOf0(v1, xO))) % 42.84/6.82 % 42.84/6.82 Further assumptions not needed in the proof: % 42.84/6.82 -------------------------------------------- % 42.84/6.82 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 42.84/6.82 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 42.84/6.82 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 42.84/6.82 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 42.84/6.82 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 42.84/6.82 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 42.84/6.82 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 42.84/6.82 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 42.84/6.82 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSuccEquSucc, % 42.84/6.82 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3453, % 42.84/6.82 m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, % 42.84/6.82 m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4908, % 42.84/6.82 m__4982, m__5106 % 42.84/6.82 % 42.84/6.82 Those formulas are unsatisfiable: % 42.84/6.82 --------------------------------- % 42.84/6.82 % 42.84/6.82 Begin of proof % 42.84/6.82 | % 42.84/6.82 | ALPHA: (m__3435) implies: % 42.84/6.82 | (1) aSet0(xS) % 42.84/6.82 | % 42.84/6.82 | ALPHA: (m__4891) implies: % 42.84/6.83 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 42.84/6.83 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 42.84/6.83 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 42.84/6.83 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 42.84/6.83 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 42.84/6.83 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 42.84/6.83 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 42.84/6.83 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 42.84/6.83 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 42.84/6.83 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 42.84/6.83 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 42.84/6.83 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 42.84/6.83 | $i(v4) & aElementOf0(v4, v1)))) % 42.84/6.83 | % 42.84/6.83 | ALPHA: (m__4998) implies: % 42.84/6.83 | (3) aSubsetOf0(xO, xS) % 42.84/6.83 | % 42.84/6.83 | ALPHA: (m__5078) implies: % 42.84/6.83 | (4) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) & % 42.84/6.83 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 42.84/6.83 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 42.84/6.83 | % 42.84/6.83 | ALPHA: (m__5093) implies: % 42.84/6.83 | (5) $i(xO) % 42.84/6.83 | % 42.84/6.83 | ALPHA: (m__) implies: % 42.84/6.83 | (6) $i(xS) % 42.84/6.83 | (7) $i(xQ) % 42.84/6.83 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzozmdt0(xc) = v0 & $i(v2) % 42.84/6.83 | & $i(v1) & $i(v0) & aElementOf0(v2, xQ) & aElementOf0(v1, xQ) & ~ % 42.84/6.83 | aSubsetOf0(xQ, xS) & ~ aElementOf0(v2, xS) & ~ aElementOf0(v1, xS) % 42.84/6.83 | & ~ aElementOf0(xQ, v0)) % 42.84/6.83 | % 42.84/6.83 | DELTA: instantiating (4) with fresh symbol all_82_0 gives: % 42.84/6.83 | (9) slbdtsldtrb0(xO, xK) = all_82_0 & sbrdtbr0(xQ) = xK & $i(all_82_0) & % 42.84/6.83 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_82_0) & aSet0(xQ) & ! [v0: % 42.84/6.83 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 42.84/6.83 | % 42.84/6.83 | ALPHA: (9) implies: % 42.84/6.83 | (10) aSet0(xQ) % 42.84/6.83 | (11) aSubsetOf0(xQ, xO) % 42.84/6.83 | % 42.84/6.83 | DELTA: instantiating (8) with fresh symbols all_85_0, all_85_1, all_85_2 % 42.84/6.83 | gives: % 42.84/6.83 | (12) szDzozmdt0(xc) = all_85_2 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) % 42.84/6.83 | & aElementOf0(all_85_0, xQ) & aElementOf0(all_85_1, xQ) & ~ % 42.84/6.84 | aSubsetOf0(xQ, xS) & ~ aElementOf0(all_85_0, xS) & ~ % 42.84/6.84 | aElementOf0(all_85_1, xS) & ~ aElementOf0(xQ, all_85_2) % 42.84/6.84 | % 42.84/6.84 | ALPHA: (12) implies: % 42.84/6.84 | (13) ~ aSubsetOf0(xQ, xS) % 42.84/6.84 | % 42.84/6.84 | DELTA: instantiating (2) with fresh symbols all_96_0, all_96_1, all_96_2 % 42.84/6.84 | gives: % 42.84/6.84 | (14) szDzizrdt0(xd) = all_96_2 & sdtlcdtrc0(xe, all_96_1) = xO & % 42.84/6.84 | sdtlbdtrb0(xd, all_96_2) = all_96_1 & szDzozmdt0(xd) = all_96_0 & % 42.84/6.84 | $i(all_96_0) & $i(all_96_1) & $i(all_96_2) & aSet0(all_96_1) & % 42.84/6.84 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_96_2 | ~ % 42.84/6.84 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 42.84/6.84 | all_96_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = % 42.84/6.84 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_96_1) | aElementOf0(v0, % 42.84/6.84 | all_96_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v1) = % 42.84/6.84 | v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_96_1) | % 42.84/6.84 | aElementOf0(v0, xO)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = % 42.84/6.84 | all_96_2) | ~ $i(v0) | ~ aElementOf0(v0, all_96_0) | % 42.84/6.84 | aElementOf0(v0, all_96_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 42.84/6.84 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 42.84/6.84 | $i(v1) & aElementOf0(v1, all_96_1))) % 42.84/6.84 | % 42.84/6.84 | ALPHA: (14) implies: % 42.84/6.84 | (15) aSet0(xO) % 42.84/6.84 | % 42.84/6.84 | GROUND_INST: instantiating (mSubTrans) with xQ, xO, xS, simplifying with (1), % 42.84/6.84 | (3), (5), (6), (7), (10), (11), (13), (15) gives: % 42.84/6.84 | (16) $false % 42.84/6.84 | % 42.84/6.84 | CLOSE: (16) is inconsistent. % 42.84/6.84 | % 42.84/6.84 End of proof % 42.84/6.84 % SZS output end Proof for theBenchmark % 42.84/6.84 % 42.84/6.84 6197ms %------------------------------------------------------------------------------