%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM625+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 : n025.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 11:49:03 EDT 2023 % Result : Theorem 39.44s 5.96s % Output : Proof 50.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM625+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 11:07:52 EDT 2023 % 0.13/0.34 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.04/1.38 Prover 1: Preprocessing ... % 5.04/1.38 Prover 4: Preprocessing ... % 5.04/1.42 Prover 2: Preprocessing ... % 5.04/1.42 Prover 3: Preprocessing ... % 5.04/1.42 Prover 6: Preprocessing ... % 5.04/1.42 Prover 0: Preprocessing ... % 5.04/1.42 Prover 5: Preprocessing ... % 14.03/2.64 Prover 1: Constructing countermodel ... % 14.73/2.68 Prover 3: Constructing countermodel ... % 14.99/2.74 Prover 6: Proving ... % 16.09/2.87 Prover 5: Proving ... % 16.96/2.98 Prover 2: Proving ... % 20.69/3.53 Prover 4: Constructing countermodel ... % 22.09/3.66 Prover 0: Proving ... % 39.44/5.96 Prover 0: proved (5319ms) % 39.44/5.96 % 39.44/5.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 39.44/5.96 % 39.44/5.96 Prover 2: stopped % 39.44/5.96 Prover 6: stopped % 39.92/5.98 Prover 5: stopped % 39.92/5.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 39.92/5.99 Prover 3: stopped % 39.92/6.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.92/6.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.92/6.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.92/6.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 42.28/6.35 Prover 7: Preprocessing ... % 43.02/6.38 Prover 8: Preprocessing ... % 43.02/6.39 Prover 10: Preprocessing ... % 43.02/6.43 Prover 11: Preprocessing ... % 43.02/6.46 Prover 13: Preprocessing ... % 44.86/6.63 Prover 7: Constructing countermodel ... % 44.86/6.64 Prover 10: Constructing countermodel ... % 45.61/6.74 Prover 8: Warning: ignoring some quantifiers % 45.61/6.75 Prover 8: Constructing countermodel ... % 46.29/6.82 Prover 13: Warning: ignoring some quantifiers % 46.29/6.84 Prover 13: Constructing countermodel ... % 48.68/7.18 Prover 10: Found proof (size 33) % 48.68/7.18 Prover 10: proved (1203ms) % 48.68/7.18 Prover 13: stopped % 48.68/7.18 Prover 8: stopped % 48.68/7.18 Prover 7: stopped % 48.68/7.18 Prover 1: stopped % 48.68/7.18 Prover 4: stopped % 49.90/7.33 Prover 11: Constructing countermodel ... % 49.90/7.36 Prover 11: stopped % 49.90/7.36 % 49.90/7.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 49.90/7.36 % 49.90/7.36 % SZS output start Proof for theBenchmark % 49.90/7.37 Assumptions after simplification: % 49.90/7.37 --------------------------------- % 49.90/7.37 % 49.90/7.37 (mDefDiff) % 49.90/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 49.90/7.40 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 49.90/7.40 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 49.90/7.40 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 49.90/7.40 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 49.90/7.40 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 49.90/7.40 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 49.90/7.40 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 49.90/7.40 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 49.90/7.40 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 49.90/7.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 49.90/7.40 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 49.90/7.40 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 49.90/7.40 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 49.90/7.40 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 49.90/7.40 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 49.90/7.40 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 49.90/7.40 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 49.90/7.40 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 49.90/7.40 % 49.90/7.40 (mDefSub) % 50.30/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 50.30/7.40 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 50.30/7.40 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 50.30/7.40 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 50.30/7.40 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 50.30/7.40 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 50.30/7.40 % 50.30/7.40 (mImgElm) % 50.30/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0, % 50.30/7.40 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 50.30/7.40 aFunction0(v0) | ~ aElementOf0(v2, v1) | aElement0(v3)) % 50.30/7.40 % 50.30/7.40 (m__4660) % 50.30/7.41 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 50.30/7.41 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 50.30/7.41 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 50.30/7.41 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 50.30/7.41 % 50.30/7.41 (m__4891) % 50.30/7.41 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 50.30/7.41 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 50.30/7.41 aSet0(xO)) % 50.30/7.41 % 50.30/7.41 (m__5093) % 50.30/7.41 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO) % 50.30/7.41 % 50.30/7.41 (m__5147) % 50.30/7.41 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) % 50.30/7.41 % 50.30/7.41 (m__5164) % 50.30/7.41 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 50.30/7.41 $i(v0) & aSet0(xP)) % 50.30/7.41 % 50.30/7.41 (m__5309) % 50.30/7.41 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 50.30/7.41 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp & % 50.30/7.41 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0)) % 50.30/7.41 % 50.30/7.41 (m__5348) % 50.30/7.41 $i(xx) & $i(xP) & aElementOf0(xx, xP) % 50.30/7.41 % 50.30/7.41 (m__5365) % 50.30/7.41 $i(xx) & $i(xO) & $i(szNzAzT0) & aElementOf0(xx, xO) & aElementOf0(xx, % 50.30/7.41 szNzAzT0) % 50.30/7.41 % 50.30/7.41 (m__5389) % 50.30/7.41 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 50.30/7.41 aElementOf0(xm, szNzAzT0) % 50.30/7.41 % 50.30/7.41 (m__5461) % 50.30/7.41 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 50.30/7.41 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)) % 50.30/7.41 % 50.30/7.41 (m__5481) % 50.30/7.41 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) % 50.30/7.41 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0)) % 50.30/7.41 % 50.30/7.41 (m__5496) % 50.30/7.41 xx = xp & $i(xp) % 50.30/7.41 % 50.30/7.41 (function-axioms) % 50.30/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.30/7.42 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 50.30/7.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 50.30/7.42 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 50.30/7.42 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 50.30/7.42 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 50.30/7.42 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 50.30/7.42 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 50.30/7.42 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 50.30/7.42 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 50.30/7.42 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 50.30/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 50.30/7.42 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 50.30/7.42 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 50.30/7.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.30/7.42 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 50.30/7.42 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.30/7.42 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 50.30/7.42 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 50.30/7.42 v0)) % 50.30/7.42 % 50.30/7.42 Further assumptions not needed in the proof: % 50.30/7.42 -------------------------------------------- % 50.30/7.42 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 50.30/7.42 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 50.30/7.42 mDefCons, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, % 50.30/7.42 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 50.30/7.42 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgRng, % 50.30/7.42 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, % 50.30/7.42 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 50.30/7.42 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 50.30/7.42 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 50.30/7.42 mZeroLess, mZeroNum, m__, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 50.30/7.42 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, % 50.30/7.42 m__4331, m__4411, m__4618, m__4730, m__4758, m__4854, m__4908, m__4982, m__4998, % 50.30/7.42 m__5078, m__5106, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, % 50.30/7.42 m__5321, m__5401, m__5442 % 50.30/7.42 % 50.30/7.42 Those formulas are unsatisfiable: % 50.30/7.42 --------------------------------- % 50.30/7.42 % 50.30/7.42 Begin of proof % 50.30/7.42 | % 50.30/7.42 | ALPHA: (mDefSub) implies: % 50.30/7.42 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 50.30/7.42 | v0) | ~ aSet0(v0) | aSet0(v1)) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (mDefDiff) implies: % 50.30/7.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | % 50.30/7.42 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~ % 50.30/7.42 | aElement0(v1) | ~ aSet0(v0)) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__4660) implies: % 50.30/7.42 | (3) aFunction0(xe) % 50.30/7.42 | (4) szDzozmdt0(xe) = szNzAzT0 % 50.30/7.42 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 50.30/7.42 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 50.30/7.42 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__4891) implies: % 50.30/7.42 | (6) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = % 50.30/7.42 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__5093) implies: % 50.30/7.42 | (7) aSubsetOf0(xQ, xO) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__5147) implies: % 50.30/7.42 | (8) szmzizndt0(xQ) = xp % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__5164) implies: % 50.30/7.42 | (9) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 50.30/7.42 | aSet0(xP)) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__5309) implies: % 50.30/7.42 | (10) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 50.30/7.42 | = v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn, % 50.30/7.42 | v1) & aElementOf0(xn, szNzAzT0)) % 50.30/7.42 | % 50.30/7.42 | ALPHA: (m__5348) implies: % 50.30/7.42 | (11) aElementOf0(xx, xP) % 50.30/7.42 | (12) $i(xP) % 50.30/7.42 | % 50.30/7.43 | ALPHA: (m__5365) implies: % 50.30/7.43 | (13) $i(xO) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (m__5389) implies: % 50.30/7.43 | (14) aElementOf0(xm, szNzAzT0) % 50.30/7.43 | (15) $i(xe) % 50.30/7.43 | (16) sdtlpdtrp0(xe, xm) = xx % 50.30/7.43 | % 50.30/7.43 | ALPHA: (m__5461) implies: % 50.30/7.43 | (17) $i(xn) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (m__5481) implies: % 50.30/7.43 | (18) $i(xQ) % 50.30/7.43 | (19) $i(xm) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (m__5496) implies: % 50.30/7.43 | (20) xx = xp % 50.30/7.43 | % 50.30/7.43 | ALPHA: (function-axioms) implies: % 50.30/7.43 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.30/7.43 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 50.30/7.43 | % 50.30/7.43 | DELTA: instantiating (9) with fresh symbol all_88_0 gives: % 50.30/7.43 | (22) szmzizndt0(xQ) = all_88_0 & sdtmndt0(xQ, all_88_0) = xP & $i(all_88_0) % 50.30/7.43 | & aSet0(xP) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (22) implies: % 50.30/7.43 | (23) sdtmndt0(xQ, all_88_0) = xP % 50.30/7.43 | (24) szmzizndt0(xQ) = all_88_0 % 50.30/7.43 | % 50.30/7.43 | DELTA: instantiating (6) with fresh symbols all_94_0, all_94_1 gives: % 50.30/7.43 | (25) szDzizrdt0(xd) = all_94_1 & sdtlcdtrc0(xe, all_94_0) = xO & % 50.30/7.43 | sdtlbdtrb0(xd, all_94_1) = all_94_0 & $i(all_94_0) & $i(all_94_1) & % 50.30/7.43 | aSet0(xO) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (25) implies: % 50.30/7.43 | (26) aSet0(xO) % 50.30/7.43 | % 50.30/7.43 | DELTA: instantiating (10) with fresh symbols all_100_0, all_100_1 gives: % 50.30/7.43 | (27) szDzizrdt0(xd) = all_100_1 & sdtlbdtrb0(xd, all_100_1) = all_100_0 & % 50.30/7.43 | sdtlpdtrp0(xe, xn) = xp & $i(all_100_0) & $i(all_100_1) & % 50.30/7.43 | aElementOf0(xn, all_100_0) & aElementOf0(xn, szNzAzT0) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (27) implies: % 50.30/7.43 | (28) aElementOf0(xn, szNzAzT0) % 50.30/7.43 | (29) sdtlpdtrp0(xe, xn) = xp % 50.30/7.43 | % 50.30/7.43 | REDUCE: (16), (20) imply: % 50.30/7.43 | (30) sdtlpdtrp0(xe, xm) = xp % 50.30/7.43 | % 50.30/7.43 | REDUCE: (11), (20) imply: % 50.30/7.43 | (31) aElementOf0(xp, xP) % 50.30/7.43 | % 50.30/7.43 | GROUND_INST: instantiating (21) with xp, all_88_0, xQ, simplifying with (8), % 50.30/7.43 | (24) gives: % 50.30/7.43 | (32) all_88_0 = xp % 50.30/7.43 | % 50.30/7.43 | REDUCE: (23), (32) imply: % 50.30/7.43 | (33) sdtmndt0(xQ, xp) = xP % 50.30/7.43 | % 50.30/7.43 | GROUND_INST: instantiating (1) with xO, xQ, simplifying with (7), (13), (18), % 50.30/7.43 | (26) gives: % 50.30/7.43 | (34) aSet0(xQ) % 50.30/7.43 | % 50.30/7.43 | GROUND_INST: instantiating (5) with xn, xp, simplifying with (17), (28), (29) % 50.30/7.43 | gives: % 50.30/7.43 | (35) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp & $i(v0) % 50.30/7.43 | & $i(xp)) % 50.30/7.43 | % 50.30/7.43 | GROUND_INST: instantiating (mImgElm) with xe, szNzAzT0, xm, xp, simplifying % 50.30/7.43 | with (3), (4), (14), (15), (19), (30) gives: % 50.30/7.43 | (36) aElement0(xp) % 50.30/7.43 | % 50.30/7.43 | DELTA: instantiating (35) with fresh symbol all_128_0 gives: % 50.30/7.43 | (37) sdtlpdtrp0(xN, xn) = all_128_0 & szmzizndt0(all_128_0) = xp & % 50.30/7.43 | $i(all_128_0) & $i(xp) % 50.30/7.43 | % 50.30/7.43 | ALPHA: (37) implies: % 50.30/7.43 | (38) $i(xp) % 50.30/7.43 | % 50.30/7.44 | GROUND_INST: instantiating (2) with xQ, xp, xP, simplifying with (12), (18), % 50.30/7.44 | (31), (33), (34), (36), (38) gives: % 50.30/7.44 | (39) $false % 50.30/7.44 | % 50.30/7.44 | CLOSE: (39) is inconsistent. % 50.30/7.44 | % 50.30/7.44 End of proof % 50.30/7.44 % SZS output end Proof for theBenchmark % 50.30/7.44 % 50.30/7.44 6834ms %------------------------------------------------------------------------------