%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM609+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 : 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 11:48:56 EDT 2023 % Result : Theorem 136.46s 18.81s % Output : Proof 136.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.07 % Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.06/0.25 % Computer : n007.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Fri Aug 25 17:42:40 EDT 2023 % 0.06/0.25 % CPUTime : % 0.10/0.48 ________ _____ % 0.10/0.48 ___ __ \_________(_)________________________________ % 0.10/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.10/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.10/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.10/0.48 % 0.10/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.10/0.48 (2023-06-19) % 0.10/0.48 % 0.10/0.48 (c) Philipp Rümmer, 2009-2023 % 0.10/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.10/0.48 Amanda Stjerna. % 0.10/0.48 Free software under BSD-3-Clause. % 0.10/0.48 % 0.10/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.10/0.48 % 0.10/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.10/0.49 Running up to 7 provers in parallel. % 0.10/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.10/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.10/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.10/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.10/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.10/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.10/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.41/1.30 Prover 1: Preprocessing ... % 5.09/1.32 Prover 4: Preprocessing ... % 5.09/1.33 Prover 5: Preprocessing ... % 5.09/1.33 Prover 6: Preprocessing ... % 5.09/1.33 Prover 2: Preprocessing ... % 5.09/1.33 Prover 0: Preprocessing ... % 5.09/1.34 Prover 3: Preprocessing ... % 14.64/2.64 Prover 3: Constructing countermodel ... % 14.64/2.67 Prover 1: Constructing countermodel ... % 15.04/2.68 Prover 6: Proving ... % 15.68/2.80 Prover 5: Proving ... % 17.34/2.98 Prover 2: Proving ... % 22.99/3.77 Prover 4: Constructing countermodel ... % 24.64/3.96 Prover 0: Proving ... % 72.06/10.19 Prover 2: stopped % 72.80/10.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.98/10.39 Prover 7: Preprocessing ... % 75.59/10.64 Prover 7: Constructing countermodel ... % 99.83/13.84 Prover 5: stopped % 100.72/13.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.68/13.97 Prover 8: Preprocessing ... % 102.45/14.12 Prover 8: Warning: ignoring some quantifiers % 103.03/14.16 Prover 8: Constructing countermodel ... % 114.91/15.84 Prover 1: stopped % 114.91/15.84 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.77/15.95 Prover 9: Preprocessing ... % 121.53/16.57 Prover 9: Constructing countermodel ... % 130.33/17.79 Prover 6: stopped % 130.33/17.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 131.17/17.88 Prover 10: Preprocessing ... % 132.83/18.06 Prover 10: Constructing countermodel ... % 135.61/18.47 Prover 10: Found proof (size 43) % 135.61/18.47 Prover 10: proved (673ms) % 135.61/18.47 Prover 0: stopped % 135.61/18.47 Prover 9: stopped % 135.61/18.47 Prover 4: stopped % 135.61/18.47 Prover 8: stopped % 135.61/18.48 Prover 7: stopped % 136.46/18.80 Prover 3: stopped % 136.46/18.81 % 136.46/18.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 136.46/18.81 % 136.46/18.81 % SZS output start Proof for theBenchmark % 136.46/18.82 Assumptions after simplification: % 136.46/18.82 --------------------------------- % 136.46/18.82 % 136.46/18.82 (mDefDiff) % 136.63/18.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 136.63/18.87 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 136.63/18.87 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 136.63/18.87 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 136.63/18.87 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 136.63/18.87 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 136.63/18.87 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 136.63/18.87 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 136.63/18.87 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 136.63/18.87 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 136.63/18.87 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 136.63/18.87 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 136.63/18.87 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 136.63/18.87 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 136.63/18.87 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 136.63/18.87 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 136.63/18.87 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 136.63/18.87 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 136.63/18.87 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 136.63/18.87 % 136.63/18.87 (mDefSub) % 136.63/18.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 136.63/18.87 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 136.63/18.87 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 136.63/18.87 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 136.63/18.87 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 136.63/18.87 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 136.63/18.87 % 136.63/18.88 (mEOfElem) % 136.63/18.88 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 136.63/18.88 ~ aSet0(v0) | aElement0(v1)) % 136.63/18.88 % 136.63/18.88 (mNatExtra) % 136.63/18.88 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 136.63/18.88 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 136.63/18.88 aElementOf0(v1, szNzAzT0))) % 136.63/18.88 % 136.63/18.88 (m__) % 136.63/18.88 $i(xP) & $i(xQ) & ~ aSubsetOf0(xP, xQ) % 136.63/18.88 % 136.63/18.88 (m__3418) % 136.63/18.88 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 136.63/18.88 % 136.63/18.88 (m__3462) % 136.63/18.88 ~ (xK = sz00) & $i(xK) & $i(sz00) % 136.63/18.88 % 136.63/18.88 (m__3520) % 136.63/18.88 ~ (xK = sz00) & $i(xK) & $i(sz00) % 136.63/18.88 % 136.63/18.88 (m__4660) % 136.63/18.88 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 136.63/18.88 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 136.63/18.88 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 136.63/18.88 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 136.63/18.88 % 136.63/18.88 (m__4891) % 136.63/18.89 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 136.63/18.89 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 136.63/18.89 aSet0(xO)) % 136.63/18.89 % 136.63/18.89 (m__4982) % 136.63/18.89 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 136.63/18.89 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 136.63/18.89 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = % 136.63/18.89 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 136.63/18.89 % 136.63/18.89 (m__5078) % 136.63/18.89 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) & % 136.63/18.89 aElementOf0(xQ, v0)) % 136.63/18.89 % 136.63/18.89 (m__5093) % 136.63/18.89 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO) % 136.63/18.89 % 136.63/18.89 (m__5147) % 136.63/18.89 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) % 136.63/18.89 % 136.63/18.89 (m__5164) % 136.63/18.89 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 136.63/18.89 $i(v0) & aSet0(xP)) % 136.63/18.89 % 136.63/18.89 (m__5182) % 136.63/18.89 $i(xp) & $i(xO) & aElementOf0(xp, xO) % 136.63/18.89 % 136.63/18.89 (function-axioms) % 136.63/18.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.63/18.90 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 136.63/18.90 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 136.63/18.90 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 136.63/18.90 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 136.63/18.90 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 136.63/18.90 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 136.63/18.90 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 136.63/18.90 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 136.63/18.90 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 136.63/18.90 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 136.63/18.90 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 136.63/18.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 136.63/18.90 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 136.63/18.90 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 136.63/18.90 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 136.63/18.90 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 136.63/18.90 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 136.63/18.90 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 136.63/18.90 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 136.63/18.90 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 136.63/18.90 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 136.63/18.90 v0)) % 136.63/18.90 % 136.63/18.90 Further assumptions not needed in the proof: % 136.63/18.90 -------------------------------------------- % 136.63/18.90 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 136.63/18.90 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 136.63/18.90 mDefCons, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, % 136.63/18.90 mDefSel, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, % 136.63/18.90 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 136.63/18.90 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 136.63/18.90 mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, % 136.63/18.90 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 136.63/18.90 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 136.63/18.90 mZeroNum, m__3291, m__3398, m__3435, m__3453, m__3533, m__3623, m__3671, % 136.63/18.90 m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4730, % 136.63/18.90 m__4758, m__4854, m__4908, m__4998, m__5106, m__5116, m__5173 % 136.63/18.90 % 136.63/18.90 Those formulas are unsatisfiable: % 136.63/18.90 --------------------------------- % 136.63/18.90 % 136.63/18.90 Begin of proof % 136.63/18.90 | % 136.63/18.90 | ALPHA: (mDefSub) implies: % 136.63/18.91 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 136.63/18.91 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 136.63/18.91 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 136.63/18.91 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 136.63/18.91 | v0) | ~ aSet0(v0) | aSet0(v1)) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (mDefDiff) implies: % 136.63/18.91 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 136.63/18.91 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 136.63/18.91 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 136.63/18.91 | aElementOf0(v3, v0)) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (mNatExtra) implies: % 136.63/18.91 | (4) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 136.63/18.91 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 136.63/18.91 | szNzAzT0))) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (m__3418) implies: % 136.63/18.91 | (5) aElementOf0(xK, szNzAzT0) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (m__3520) implies: % 136.63/18.91 | (6) ~ (xK = sz00) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (m__4660) implies: % 136.63/18.91 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 136.63/18.91 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 136.63/18.91 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (m__4891) implies: % 136.63/18.91 | (8) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = % 136.63/18.91 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 136.63/18.91 | % 136.63/18.91 | ALPHA: (m__4982) implies: % 136.63/18.92 | (9) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 136.63/18.92 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 136.63/18.92 | xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & $i(v3) & % 136.63/18.92 | aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__5078) implies: % 136.63/18.92 | (10) $i(xK) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__5093) implies: % 136.63/18.92 | (11) aSubsetOf0(xQ, xO) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__5147) implies: % 136.63/18.92 | (12) szmzizndt0(xQ) = xp % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__5164) implies: % 136.63/18.92 | (13) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 136.63/18.92 | aSet0(xP)) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__5182) implies: % 136.63/18.92 | (14) aElementOf0(xp, xO) % 136.63/18.92 | (15) $i(xO) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (m__) implies: % 136.63/18.92 | (16) ~ aSubsetOf0(xP, xQ) % 136.63/18.92 | (17) $i(xQ) % 136.63/18.92 | (18) $i(xP) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (function-axioms) implies: % 136.63/18.92 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 136.63/18.92 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 136.63/18.92 | % 136.63/18.92 | DELTA: instantiating (13) with fresh symbol all_80_0 gives: % 136.63/18.92 | (20) szmzizndt0(xQ) = all_80_0 & sdtmndt0(xQ, all_80_0) = xP & $i(all_80_0) % 136.63/18.92 | & aSet0(xP) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (20) implies: % 136.63/18.92 | (21) aSet0(xP) % 136.63/18.92 | (22) $i(all_80_0) % 136.63/18.92 | (23) sdtmndt0(xQ, all_80_0) = xP % 136.63/18.92 | (24) szmzizndt0(xQ) = all_80_0 % 136.63/18.92 | % 136.63/18.92 | DELTA: instantiating (8) with fresh symbols all_84_0, all_84_1 gives: % 136.63/18.92 | (25) szDzizrdt0(xd) = all_84_1 & sdtlcdtrc0(xe, all_84_0) = xO & % 136.63/18.92 | sdtlbdtrb0(xd, all_84_1) = all_84_0 & $i(all_84_0) & $i(all_84_1) & % 136.63/18.92 | aSet0(xO) % 136.63/18.92 | % 136.63/18.92 | ALPHA: (25) implies: % 136.63/18.92 | (26) aSet0(xO) % 136.63/18.92 | % 136.63/18.92 | DELTA: instantiating (9) with fresh symbols all_90_0, all_90_1 gives: % 136.63/18.93 | (27) szDzizrdt0(xd) = all_90_1 & sdtlbdtrb0(xd, all_90_1) = all_90_0 & % 136.63/18.93 | $i(all_90_0) & $i(all_90_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 136.63/18.93 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 136.63/18.93 | $i(v1) & aElementOf0(v1, all_90_0) & aElementOf0(v1, szNzAzT0))) % 136.63/18.93 | % 136.63/18.93 | ALPHA: (27) implies: % 136.63/18.93 | (28) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : % 136.63/18.93 | (sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, all_90_0) & % 136.63/18.93 | aElementOf0(v1, szNzAzT0))) % 136.63/18.93 | % 136.63/18.93 | GROUND_INST: instantiating (19) with xp, all_80_0, xQ, simplifying with (12), % 136.63/18.93 | (24) gives: % 136.63/18.93 | (29) all_80_0 = xp % 136.63/18.93 | % 136.63/18.93 | REDUCE: (23), (29) imply: % 136.63/18.93 | (30) sdtmndt0(xQ, xp) = xP % 136.63/18.93 | % 136.63/18.93 | REDUCE: (22), (29) imply: % 136.63/18.93 | (31) $i(xp) % 136.63/18.93 | % 136.63/18.93 | GROUND_INST: instantiating (4) with xK, simplifying with (5), (10) gives: % 136.63/18.93 | (32) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 136.63/18.93 | aElementOf0(v0, szNzAzT0)) % 136.63/18.93 | % 136.63/18.93 | GROUND_INST: instantiating (mEOfElem) with xO, xp, simplifying with (14), % 136.63/18.93 | (15), (26), (31) gives: % 136.63/18.93 | (33) aElement0(xp) % 136.63/18.93 | % 136.63/18.93 | GROUND_INST: instantiating (28) with xp, simplifying with (14), (31) gives: % 136.63/18.93 | (34) ? [v0: $i] : (sdtlpdtrp0(xe, v0) = xp & $i(v0) & aElementOf0(v0, % 136.63/18.93 | all_90_0) & aElementOf0(v0, szNzAzT0)) % 136.63/18.93 | % 136.63/18.93 | GROUND_INST: instantiating (2) with xO, xQ, simplifying with (11), (15), (17), % 136.63/18.93 | (26) gives: % 136.63/18.93 | (35) aSet0(xQ) % 136.63/18.93 | % 136.63/18.93 | DELTA: instantiating (34) with fresh symbol all_114_0 gives: % 136.63/18.93 | (36) sdtlpdtrp0(xe, all_114_0) = xp & $i(all_114_0) & % 136.63/18.93 | aElementOf0(all_114_0, all_90_0) & aElementOf0(all_114_0, szNzAzT0) % 136.63/18.93 | % 136.63/18.93 | ALPHA: (36) implies: % 136.63/18.94 | (37) aElementOf0(all_114_0, szNzAzT0) % 136.63/18.94 | (38) $i(all_114_0) % 136.63/18.94 | (39) sdtlpdtrp0(xe, all_114_0) = xp % 136.63/18.94 | % 136.63/18.94 | BETA: splitting (32) gives: % 136.63/18.94 | % 136.63/18.94 | Case 1: % 136.63/18.94 | | % 136.63/18.94 | | (40) xK = sz00 % 136.63/18.94 | | % 136.63/18.94 | | REDUCE: (6), (40) imply: % 136.63/18.94 | | (41) $false % 136.63/18.94 | | % 136.63/18.94 | | CLOSE: (41) is inconsistent. % 136.63/18.94 | | % 136.63/18.94 | Case 2: % 136.63/18.94 | | % 136.63/18.94 | | % 136.63/18.94 | | GROUND_INST: instantiating (1) with xQ, xP, simplifying with (16), (17), % 136.63/18.94 | | (18), (21), (35) gives: % 136.63/18.94 | | (42) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xP) & ~ aElementOf0(v0, % 136.63/18.94 | | xQ)) % 136.63/18.94 | | % 136.63/18.94 | | GROUND_INST: instantiating (7) with all_114_0, xp, simplifying with (37), % 136.63/18.94 | | (38), (39) gives: % 136.63/18.94 | | (43) ? [v0: $i] : (sdtlpdtrp0(xN, all_114_0) = v0 & szmzizndt0(v0) = xp % 136.63/18.94 | | & $i(v0) & $i(xp)) % 136.63/18.94 | | % 136.63/18.94 | | DELTA: instantiating (42) with fresh symbol all_139_0 gives: % 136.63/18.94 | | (44) $i(all_139_0) & aElementOf0(all_139_0, xP) & ~ % 136.63/18.94 | | aElementOf0(all_139_0, xQ) % 136.63/18.94 | | % 136.63/18.94 | | ALPHA: (44) implies: % 136.63/18.94 | | (45) ~ aElementOf0(all_139_0, xQ) % 136.63/18.94 | | (46) aElementOf0(all_139_0, xP) % 136.63/18.94 | | (47) $i(all_139_0) % 136.63/18.94 | | % 136.63/18.94 | | DELTA: instantiating (43) with fresh symbol all_145_0 gives: % 136.63/18.94 | | (48) sdtlpdtrp0(xN, all_114_0) = all_145_0 & szmzizndt0(all_145_0) = xp & % 136.63/18.94 | | $i(all_145_0) & $i(xp) % 136.63/18.94 | | % 136.63/18.95 | | GROUND_INST: instantiating (3) with xQ, xp, xP, all_139_0, simplifying with % 136.63/18.95 | | (17), (18), (30), (31), (33), (35), (45), (46), (47) gives: % 136.63/18.95 | | (49) $false % 136.63/18.95 | | % 136.63/18.95 | | CLOSE: (49) is inconsistent. % 136.63/18.95 | | % 136.63/18.95 | End of split % 136.63/18.95 | % 136.63/18.95 End of proof % 136.63/18.95 % SZS output end Proof for theBenchmark % 136.63/18.95 % 136.63/18.95 18468ms %------------------------------------------------------------------------------