%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM624+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 : n016.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 23.53s 4.01s % Output : Proof 30.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM624+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n016.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 14:52:25 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.95/1.52 Prover 4: Preprocessing ... % 5.61/1.55 Prover 1: Preprocessing ... % 5.61/1.58 Prover 0: Preprocessing ... % 5.61/1.58 Prover 3: Preprocessing ... % 5.61/1.58 Prover 6: Preprocessing ... % 5.61/1.58 Prover 2: Preprocessing ... % 5.61/1.58 Prover 5: Preprocessing ... % 15.49/2.94 Prover 1: Constructing countermodel ... % 16.47/3.04 Prover 3: Constructing countermodel ... % 16.69/3.07 Prover 6: Proving ... % 17.79/3.20 Prover 5: Proving ... % 18.35/3.26 Prover 2: Proving ... % 22.94/3.89 Prover 4: Constructing countermodel ... % 23.53/4.01 Prover 3: proved (3351ms) % 23.53/4.01 % 23.53/4.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.53/4.01 % 23.53/4.01 Prover 2: stopped % 23.53/4.01 Prover 5: stopped % 23.99/4.02 Prover 6: stopped % 23.99/4.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.99/4.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.99/4.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.99/4.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.99/4.19 Prover 7: Preprocessing ... % 23.99/4.23 Prover 0: Proving ... % 23.99/4.24 Prover 10: Preprocessing ... % 25.09/4.25 Prover 0: stopped % 25.09/4.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.16/4.33 Prover 11: Preprocessing ... % 26.44/4.40 Prover 8: Preprocessing ... % 26.97/4.45 Prover 13: Preprocessing ... % 27.23/4.53 Prover 10: Constructing countermodel ... % 27.93/4.59 Prover 7: Constructing countermodel ... % 29.59/4.85 Prover 8: Warning: ignoring some quantifiers % 29.59/4.86 Prover 8: Constructing countermodel ... % 29.59/4.89 Prover 10: Found proof (size 49) % 29.59/4.89 Prover 10: proved (851ms) % 29.59/4.90 Prover 7: stopped % 29.59/4.90 Prover 1: stopped % 29.59/4.90 Prover 4: stopped % 29.59/4.90 Prover 11: stopped % 29.59/4.90 Prover 8: stopped % 29.59/4.92 Prover 13: Warning: ignoring some quantifiers % 29.59/4.95 Prover 13: Constructing countermodel ... % 29.59/4.97 Prover 13: stopped % 29.59/4.97 % 29.59/4.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 29.59/4.97 % 30.62/4.98 % SZS output start Proof for theBenchmark % 30.62/4.98 Assumptions after simplification: % 30.62/4.98 --------------------------------- % 30.62/4.98 % 30.62/4.98 (mMinMin) % 30.87/5.01 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 30.87/5.01 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ % 30.87/5.01 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) % 30.87/5.01 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2, % 30.87/5.01 v1)) % 30.87/5.01 % 30.87/5.01 (m__) % 30.87/5.01 ~ (xx = xp) & $i(xx) & $i(xp) % 30.87/5.01 % 30.87/5.01 (m__5147) % 30.87/5.01 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) % 30.87/5.01 % 30.87/5.01 (m__5164) % 30.87/5.01 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 30.87/5.01 $i(v0) & aSet0(xP)) % 30.87/5.01 % 30.87/5.01 (m__5401) % 30.87/5.01 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & % 30.87/5.01 szmzizndt0(v0) = xx & $i(v0)) % 30.87/5.01 % 30.87/5.01 (m__5442) % 30.87/5.01 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 30.87/5.01 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & % 30.87/5.01 $i(v2) & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v2)) % 30.87/5.01 % 30.87/5.01 (m__5461) % 30.87/5.01 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 30.87/5.01 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)) % 30.87/5.01 % 30.87/5.01 (m__5481) % 30.87/5.01 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) % 30.87/5.01 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0)) % 30.87/5.01 % 30.87/5.01 (m__5518) % 30.87/5.01 $i(xm) & $i(xQ) & $i(xN) & $i(szNzAzT0) & $i(slcrc0) & ? [v0: $i] : ( ~ (v0 = % 30.87/5.01 slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm) = v0 & $i(v0) & % 30.87/5.01 aSubsetOf0(v0, szNzAzT0) & aSubsetOf0(xQ, szNzAzT0)) % 30.87/5.01 % 30.87/5.01 (function-axioms) % 30.87/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.87/5.02 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.87/5.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 30.87/5.02 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 30.87/5.02 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 30.87/5.02 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 30.87/5.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 30.87/5.02 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 30.87/5.02 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 30.87/5.02 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 30.87/5.02 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 30.87/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 30.87/5.02 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 30.87/5.02 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 30.87/5.02 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 30.87/5.02 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 30.87/5.02 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 30.87/5.02 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 30.87/5.02 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 30.87/5.02 v0)) % 30.87/5.02 % 30.87/5.02 Further assumptions not needed in the proof: % 30.87/5.02 -------------------------------------------- % 30.87/5.02 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 30.87/5.02 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 30.87/5.02 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 30.87/5.02 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 30.87/5.02 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 30.87/5.02 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 30.87/5.02 mLessTotal, mLessTrans, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, % 30.87/5.02 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, % 30.87/5.02 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, % 30.87/5.02 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, % 30.87/5.02 m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, % 30.87/5.02 m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, % 30.87/5.02 m__4891, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5173, % 30.87/5.02 m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, m__5321, m__5348, m__5365, % 30.87/5.02 m__5389 % 30.87/5.02 % 30.87/5.02 Those formulas are unsatisfiable: % 30.87/5.02 --------------------------------- % 30.87/5.02 % 30.87/5.02 Begin of proof % 30.87/5.02 | % 30.87/5.02 | ALPHA: (mMinMin) implies: % 30.87/5.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = % 30.87/5.02 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0) % 30.87/5.02 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 30.87/5.02 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ % 30.87/5.02 | aElementOf0(v2, v1)) % 30.87/5.02 | % 30.87/5.02 | ALPHA: (m__5147) implies: % 30.87/5.02 | (2) szmzizndt0(xQ) = xp % 30.87/5.02 | % 30.87/5.02 | ALPHA: (m__5164) implies: % 30.87/5.03 | (3) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 30.87/5.03 | aSet0(xP)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__5401) implies: % 30.87/5.03 | (4) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & $i(v0)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__5442) implies: % 30.87/5.03 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 & % 30.87/5.03 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) & % 30.87/5.03 | $i(v0) & ~ aSubsetOf0(v0, v2)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__5461) implies: % 30.87/5.03 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 30.87/5.03 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__5481) implies: % 30.87/5.03 | (7) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ) & % 30.87/5.03 | aElementOf0(xp, v0)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__5518) implies: % 30.87/5.03 | (8) $i(xQ) % 30.87/5.03 | (9) ? [v0: $i] : ( ~ (v0 = slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm) % 30.87/5.03 | = v0 & $i(v0) & aSubsetOf0(v0, szNzAzT0) & aSubsetOf0(xQ, szNzAzT0)) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (m__) implies: % 30.87/5.03 | (10) ~ (xx = xp) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (function-axioms) implies: % 30.87/5.03 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 30.87/5.03 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 30.87/5.03 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.87/5.03 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (4) with fresh symbol all_80_0 gives: % 30.87/5.03 | (13) sdtlpdtrp0(xN, xm) = all_80_0 & szmzizndt0(all_80_0) = xx & % 30.87/5.03 | $i(all_80_0) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (13) implies: % 30.87/5.03 | (14) szmzizndt0(all_80_0) = xx % 30.87/5.03 | (15) sdtlpdtrp0(xN, xm) = all_80_0 % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (3) with fresh symbol all_86_0 gives: % 30.87/5.03 | (16) szmzizndt0(xQ) = all_86_0 & sdtmndt0(xQ, all_86_0) = xP & $i(all_86_0) % 30.87/5.03 | & aSet0(xP) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (16) implies: % 30.87/5.03 | (17) szmzizndt0(xQ) = all_86_0 % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (7) with fresh symbol all_88_0 gives: % 30.87/5.03 | (18) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & aElementOf0(xx, xQ) & % 30.87/5.03 | aElementOf0(xp, all_88_0) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (18) implies: % 30.87/5.03 | (19) aElementOf0(xp, all_88_0) % 30.87/5.03 | (20) aElementOf0(xx, xQ) % 30.87/5.03 | (21) $i(all_88_0) % 30.87/5.03 | (22) sdtlpdtrp0(xN, xm) = all_88_0 % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (6) with fresh symbols all_90_0, all_90_1 gives: % 30.87/5.03 | (23) sdtlpdtrp0(xN, xm) = all_90_0 & sdtlpdtrp0(xN, xn) = all_90_1 & % 30.87/5.03 | $i(all_90_0) & $i(all_90_1) & aSubsetOf0(all_90_1, all_90_0) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (23) implies: % 30.87/5.03 | (24) sdtlpdtrp0(xN, xm) = all_90_0 % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (9) with fresh symbol all_94_0 gives: % 30.87/5.03 | (25) ~ (all_94_0 = slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm) = % 30.87/5.03 | all_94_0 & $i(all_94_0) & aSubsetOf0(all_94_0, szNzAzT0) & % 30.87/5.03 | aSubsetOf0(xQ, szNzAzT0) % 30.87/5.03 | % 30.87/5.03 | ALPHA: (25) implies: % 30.87/5.03 | (26) ~ (xQ = slcrc0) % 30.87/5.03 | (27) ~ (all_94_0 = slcrc0) % 30.87/5.03 | (28) aSubsetOf0(xQ, szNzAzT0) % 30.87/5.03 | (29) aSubsetOf0(all_94_0, szNzAzT0) % 30.87/5.03 | (30) sdtlpdtrp0(xN, xm) = all_94_0 % 30.87/5.03 | % 30.87/5.03 | DELTA: instantiating (5) with fresh symbols all_104_0, all_104_1, all_104_2 % 30.87/5.03 | gives: % 30.87/5.04 | (31) sdtlpdtrp0(xN, all_104_1) = all_104_0 & sdtlpdtrp0(xN, xm) = all_104_2 % 30.87/5.04 | & szszuzczcdt0(xn) = all_104_1 & $i(all_104_0) & $i(all_104_1) & % 30.87/5.04 | $i(all_104_2) & ~ aSubsetOf0(all_104_2, all_104_0) % 30.87/5.04 | % 30.87/5.04 | ALPHA: (31) implies: % 30.87/5.04 | (32) sdtlpdtrp0(xN, xm) = all_104_2 % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (11) with xp, all_86_0, xQ, simplifying with (2), % 30.87/5.04 | (17) gives: % 30.87/5.04 | (33) all_86_0 = xp % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (12) with all_80_0, all_94_0, xm, xN, simplifying % 30.87/5.04 | with (15), (30) gives: % 30.87/5.04 | (34) all_94_0 = all_80_0 % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (12) with all_94_0, all_104_2, xm, xN, simplifying % 30.87/5.04 | with (30), (32) gives: % 30.87/5.04 | (35) all_104_2 = all_94_0 % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (12) with all_90_0, all_104_2, xm, xN, simplifying % 30.87/5.04 | with (24), (32) gives: % 30.87/5.04 | (36) all_104_2 = all_90_0 % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (12) with all_88_0, all_104_2, xm, xN, simplifying % 30.87/5.04 | with (22), (32) gives: % 30.87/5.04 | (37) all_104_2 = all_88_0 % 30.87/5.04 | % 30.87/5.04 | COMBINE_EQS: (35), (36) imply: % 30.87/5.04 | (38) all_94_0 = all_90_0 % 30.87/5.04 | % 30.87/5.04 | SIMP: (38) implies: % 30.87/5.04 | (39) all_94_0 = all_90_0 % 30.87/5.04 | % 30.87/5.04 | COMBINE_EQS: (36), (37) imply: % 30.87/5.04 | (40) all_90_0 = all_88_0 % 30.87/5.04 | % 30.87/5.04 | COMBINE_EQS: (34), (39) imply: % 30.87/5.04 | (41) all_90_0 = all_80_0 % 30.87/5.04 | % 30.87/5.04 | SIMP: (41) implies: % 30.87/5.04 | (42) all_90_0 = all_80_0 % 30.87/5.04 | % 30.87/5.04 | COMBINE_EQS: (40), (42) imply: % 30.87/5.04 | (43) all_88_0 = all_80_0 % 30.87/5.04 | % 30.87/5.04 | SIMP: (43) implies: % 30.87/5.04 | (44) all_88_0 = all_80_0 % 30.87/5.04 | % 30.87/5.04 | REDUCE: (27), (34) imply: % 30.87/5.04 | (45) ~ (all_80_0 = slcrc0) % 30.87/5.04 | % 30.87/5.04 | REDUCE: (21), (44) imply: % 30.87/5.04 | (46) $i(all_80_0) % 30.87/5.04 | % 30.87/5.04 | REDUCE: (29), (34) imply: % 30.87/5.04 | (47) aSubsetOf0(all_80_0, szNzAzT0) % 30.87/5.04 | % 30.87/5.04 | REDUCE: (19), (44) imply: % 30.87/5.04 | (48) aElementOf0(xp, all_80_0) % 30.87/5.04 | % 30.87/5.04 | GROUND_INST: instantiating (1) with xQ, all_80_0, xp, xx, simplifying with % 30.87/5.04 | (2), (8), (14), (20), (28), (46), (47), (48) gives: % 30.87/5.04 | (49) all_80_0 = slcrc0 | xx = xp | xQ = slcrc0 % 30.87/5.04 | % 30.87/5.04 | BETA: splitting (49) gives: % 30.87/5.04 | % 30.87/5.04 | Case 1: % 30.87/5.04 | | % 30.87/5.04 | | (50) all_80_0 = slcrc0 % 30.87/5.04 | | % 30.87/5.04 | | REDUCE: (45), (50) imply: % 30.87/5.04 | | (51) $false % 30.87/5.04 | | % 30.87/5.04 | | CLOSE: (51) is inconsistent. % 30.87/5.04 | | % 30.87/5.04 | Case 2: % 30.87/5.04 | | % 30.87/5.04 | | (52) xx = xp | xQ = slcrc0 % 30.87/5.04 | | % 30.87/5.04 | | BETA: splitting (52) gives: % 30.87/5.04 | | % 30.87/5.04 | | Case 1: % 30.87/5.04 | | | % 30.87/5.04 | | | (53) xQ = slcrc0 % 30.87/5.04 | | | % 30.87/5.04 | | | REDUCE: (26), (53) imply: % 30.87/5.04 | | | (54) $false % 30.87/5.04 | | | % 30.87/5.04 | | | CLOSE: (54) is inconsistent. % 30.87/5.04 | | | % 30.87/5.04 | | Case 2: % 30.87/5.04 | | | % 30.87/5.04 | | | (55) xx = xp % 30.87/5.04 | | | % 30.87/5.04 | | | REDUCE: (10), (55) imply: % 30.87/5.04 | | | (56) $false % 30.87/5.04 | | | % 30.87/5.04 | | | CLOSE: (56) is inconsistent. % 30.87/5.04 | | | % 30.87/5.04 | | End of split % 30.87/5.04 | | % 30.87/5.04 | End of split % 30.87/5.04 | % 30.87/5.04 End of proof % 30.87/5.04 % SZS output end Proof for theBenchmark % 30.87/5.04 % 30.87/5.04 4416ms %------------------------------------------------------------------------------