%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM615+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 : n024.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 11:48:59 EDT 2023 % Result : Theorem 26.81s 4.30s % Output : Proof 70.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM615+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n024.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 12:38:39 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.18/1.71 Prover 1: Preprocessing ... % 7.18/1.72 Prover 0: Preprocessing ... % 7.18/1.72 Prover 5: Preprocessing ... % 7.18/1.72 Prover 2: Preprocessing ... % 7.18/1.72 Prover 3: Preprocessing ... % 7.18/1.72 Prover 6: Preprocessing ... % 7.41/1.76 Prover 4: Preprocessing ... % 18.85/3.27 Prover 1: Constructing countermodel ... % 18.85/3.28 Prover 6: Proving ... % 19.34/3.34 Prover 3: Constructing countermodel ... % 21.96/3.71 Prover 5: Proving ... % 26.41/4.29 Prover 3: proved (3659ms) % 26.41/4.30 % 26.81/4.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.81/4.30 % 26.81/4.30 Prover 5: stopped % 26.81/4.30 Prover 6: stopped % 26.81/4.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.81/4.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.81/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 28.75/4.60 Prover 8: Preprocessing ... % 29.20/4.62 Prover 10: Preprocessing ... % 29.20/4.63 Prover 7: Preprocessing ... % 32.35/5.09 Prover 8: Warning: ignoring some quantifiers % 33.03/5.11 Prover 8: Constructing countermodel ... % 35.42/5.44 Prover 10: Constructing countermodel ... % 39.08/6.02 Prover 7: Constructing countermodel ... % 44.82/6.67 Prover 4: Constructing countermodel ... % 50.24/7.41 Prover 2: Proving ... % 50.87/7.44 Prover 2: stopped % 50.87/7.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 51.26/7.52 Prover 0: Proving ... % 51.26/7.55 Prover 0: stopped % 51.96/7.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 53.62/7.82 Prover 11: Preprocessing ... % 53.62/7.89 Prover 13: Preprocessing ... % 62.32/8.91 Prover 13: Warning: ignoring some quantifiers % 63.43/9.06 Prover 13: Constructing countermodel ... % 64.63/9.22 Prover 7: Found proof (size 30) % 64.63/9.23 Prover 7: proved (4927ms) % 64.63/9.23 Prover 1: stopped % 64.63/9.24 Prover 4: stopped % 64.63/9.24 Prover 8: stopped % 64.63/9.24 Prover 13: stopped % 64.63/9.25 Prover 10: stopped % 70.14/10.57 Prover 11: Constructing countermodel ... % 70.14/10.61 Prover 11: stopped % 70.14/10.61 % 70.14/10.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 70.14/10.61 % 70.53/10.62 % SZS output start Proof for theBenchmark % 70.53/10.63 Assumptions after simplification: % 70.53/10.63 --------------------------------- % 70.53/10.63 % 70.53/10.63 (mCountNFin_01) % 70.53/10.64 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 70.53/10.64 % 70.53/10.64 (mDefEmp) % 70.53/10.64 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 70.53/10.64 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 70.53/10.64 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 70.53/10.64 % 70.53/10.65 (m__) % 70.53/10.70 $i(xp) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 70.53/10.70 (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & szDzozmdt0(xd) = v0 & $i(v2) % 70.53/10.70 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = % 70.53/10.70 v4) | ~ $i(v3) | ~ aElementOf0(v3, v2) | ? [v5: $i] : ( ~ (v5 = xp) & % 70.53/10.70 sdtlpdtrp0(xe, v3) = v5 & $i(v5))) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, % 70.53/10.70 v3) = v1) | ~ $i(v3) | ~ aElementOf0(v3, v0) | ? [v4: $i] : ( ~ (v4 % 70.53/10.70 = xp) & sdtlpdtrp0(xe, v3) = v4 & $i(v4))) & ! [v3: $i] : ( ~ % 70.53/10.70 (sdtlpdtrp0(xe, v3) = xp) | ~ $i(v3) | ~ aElementOf0(v3, v2)) & ! [v3: % 70.53/10.70 $i] : ( ~ (sdtlpdtrp0(xe, v3) = xp) | ~ $i(v3) | ~ aElementOf0(v3, v0) | % 70.53/10.70 ? [v4: $i] : ( ~ (v4 = v1) & sdtlpdtrp0(xd, v3) = v4 & $i(v4)))) % 70.53/10.70 % 70.53/10.70 (m__4891) % 70.53/10.71 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 70.53/10.71 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 70.53/10.71 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 70.53/10.71 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 70.53/10.71 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 70.53/10.71 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 70.53/10.71 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 70.53/10.71 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 70.53/10.71 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 70.53/10.71 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 70.53/10.71 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 70.53/10.71 aElementOf0(v4, v1)))) % 70.53/10.71 % 70.53/10.71 (m__5182) % 70.53/10.71 $i(xp) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 70.53/10.71 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xp & % 70.53/10.71 $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, v1)) % 70.53/10.71 % 70.53/10.71 (function-axioms) % 70.53/10.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.53/10.72 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 70.53/10.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 70.53/10.72 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 70.53/10.72 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 70.53/10.72 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 70.53/10.72 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 70.53/10.72 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 70.53/10.72 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 70.53/10.72 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 70.53/10.72 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 70.53/10.72 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 70.53/10.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 70.53/10.72 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 70.53/10.72 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 70.53/10.72 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 70.53/10.72 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 70.53/10.72 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 70.53/10.72 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 70.53/10.72 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 70.53/10.72 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 70.53/10.72 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 70.53/10.72 v0)) % 70.53/10.72 % 70.53/10.72 Further assumptions not needed in the proof: % 70.53/10.72 -------------------------------------------- % 70.53/10.72 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 70.53/10.72 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 70.53/10.72 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 70.53/10.72 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 70.53/10.72 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 70.53/10.72 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 70.53/10.72 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 70.53/10.72 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 70.53/10.72 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 70.53/10.72 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 70.53/10.72 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, % 70.53/10.72 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4908, m__4982, % 70.53/10.72 m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173, m__5195, % 70.53/10.72 m__5208, m__5217, m__5270 % 70.53/10.72 % 70.53/10.72 Those formulas are unsatisfiable: % 70.53/10.72 --------------------------------- % 70.53/10.73 % 70.53/10.73 Begin of proof % 70.53/10.73 | % 70.53/10.73 | ALPHA: (mDefEmp) implies: % 70.53/10.73 | (1) aSet0(slcrc0) % 70.53/10.73 | % 70.53/10.73 | ALPHA: (mCountNFin_01) implies: % 70.53/10.73 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 70.53/10.73 | % 70.53/10.73 | ALPHA: (m__4891) implies: % 70.53/10.73 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 70.53/10.73 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 70.53/10.73 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 70.53/10.73 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 70.53/10.73 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 70.53/10.73 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 70.53/10.73 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 70.53/10.73 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 70.53/10.73 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 70.53/10.73 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 70.53/10.73 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 70.53/10.73 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 70.53/10.73 | $i(v4) & aElementOf0(v4, v1)))) % 70.53/10.73 | % 70.53/10.73 | ALPHA: (m__5182) implies: % 70.53/10.73 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 70.53/10.73 | sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xp & $i(v2) & $i(v1) & % 70.53/10.73 | $i(v0) & aElementOf0(v2, v1)) % 70.53/10.73 | % 70.53/10.73 | ALPHA: (m__) implies: % 70.53/10.73 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 & % 70.53/10.73 | sdtlbdtrb0(xd, v1) = v2 & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & % 70.53/10.73 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | % 70.53/10.74 | ~ $i(v3) | ~ aElementOf0(v3, v2) | ? [v5: $i] : ( ~ (v5 = xp) & % 70.53/10.74 | sdtlpdtrp0(xe, v3) = v5 & $i(v5))) & ! [v3: $i] : ( ~ % 70.53/10.74 | (sdtlpdtrp0(xd, v3) = v1) | ~ $i(v3) | ~ aElementOf0(v3, v0) | ? % 70.53/10.74 | [v4: $i] : ( ~ (v4 = xp) & sdtlpdtrp0(xe, v3) = v4 & $i(v4))) & ! % 70.53/10.74 | [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = xp) | ~ $i(v3) | ~ % 70.53/10.74 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = xp) % 70.53/10.74 | | ~ $i(v3) | ~ aElementOf0(v3, v0) | ? [v4: $i] : ( ~ (v4 = v1) % 70.53/10.74 | & sdtlpdtrp0(xd, v3) = v4 & $i(v4)))) % 70.53/10.74 | % 70.53/10.74 | ALPHA: (function-axioms) implies: % 70.53/10.74 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) % 70.53/10.74 | = v1) | ~ (szDzizrdt0(v2) = v0)) % 70.53/10.74 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.53/10.74 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 70.53/10.74 | % 70.53/10.74 | DELTA: instantiating (4) with fresh symbols all_90_0, all_90_1, all_90_2 % 70.53/10.74 | gives: % 70.53/10.74 | (8) szDzizrdt0(xd) = all_90_2 & sdtlbdtrb0(xd, all_90_2) = all_90_1 & % 70.53/10.74 | sdtlpdtrp0(xe, all_90_0) = xp & $i(all_90_0) & $i(all_90_1) & % 70.53/10.74 | $i(all_90_2) & aElementOf0(all_90_0, all_90_1) % 70.53/10.74 | % 70.53/10.74 | ALPHA: (8) implies: % 70.53/10.74 | (9) aElementOf0(all_90_0, all_90_1) % 70.53/10.74 | (10) $i(all_90_0) % 70.53/10.74 | (11) sdtlpdtrp0(xe, all_90_0) = xp % 70.53/10.74 | (12) sdtlbdtrb0(xd, all_90_2) = all_90_1 % 70.53/10.74 | (13) szDzizrdt0(xd) = all_90_2 % 70.53/10.74 | % 70.53/10.74 | DELTA: instantiating (5) with fresh symbols all_107_0, all_107_1, all_107_2 % 70.53/10.74 | gives: % 70.53/10.74 | (14) szDzizrdt0(xd) = all_107_1 & sdtlbdtrb0(xd, all_107_1) = all_107_0 & % 70.53/10.74 | szDzozmdt0(xd) = all_107_2 & $i(all_107_0) & $i(all_107_1) & % 70.53/10.74 | $i(all_107_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = % 70.53/10.74 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_107_0) | ? [v2: $i] : ( % 70.53/10.74 | ~ (v2 = xp) & sdtlpdtrp0(xe, v0) = v2 & $i(v2))) & ! [v0: $i] : ( % 70.53/10.74 | ~ (sdtlpdtrp0(xd, v0) = all_107_1) | ~ $i(v0) | ~ aElementOf0(v0, % 70.53/10.74 | all_107_2) | ? [v1: $i] : ( ~ (v1 = xp) & sdtlpdtrp0(xe, v0) = v1 % 70.53/10.74 | & $i(v1))) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xp) | ~ % 70.53/10.74 | $i(v0) | ~ aElementOf0(v0, all_107_0)) & ! [v0: $i] : ( ~ % 70.53/10.74 | (sdtlpdtrp0(xe, v0) = xp) | ~ $i(v0) | ~ aElementOf0(v0, % 70.53/10.74 | all_107_2) | ? [v1: any] : ( ~ (v1 = all_107_1) & sdtlpdtrp0(xd, % 70.53/10.74 | v0) = v1 & $i(v1))) % 70.53/10.74 | % 70.53/10.74 | ALPHA: (14) implies: % 70.53/10.74 | (15) sdtlbdtrb0(xd, all_107_1) = all_107_0 % 70.53/10.74 | (16) szDzizrdt0(xd) = all_107_1 % 70.53/10.74 | (17) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xp) | ~ $i(v0) | ~ % 70.53/10.74 | aElementOf0(v0, all_107_0)) % 70.53/10.74 | % 70.53/10.74 | DELTA: instantiating (3) with fresh symbols all_110_0, all_110_1, all_110_2 % 70.53/10.74 | gives: % 70.53/10.75 | (18) szDzizrdt0(xd) = all_110_2 & sdtlcdtrc0(xe, all_110_1) = xO & % 70.53/10.75 | sdtlbdtrb0(xd, all_110_2) = all_110_1 & szDzozmdt0(xd) = all_110_0 & % 70.53/10.75 | $i(all_110_0) & $i(all_110_1) & $i(all_110_2) & aSet0(all_110_1) & % 70.53/10.75 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_110_2 | ~ % 70.53/10.75 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 70.53/10.75 | all_110_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 70.53/10.75 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_110_1) | % 70.53/10.75 | aElementOf0(v0, all_110_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.53/10.75 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 70.53/10.75 | aElementOf0(v1, all_110_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 70.53/10.75 | ~ (sdtlpdtrp0(xd, v0) = all_110_2) | ~ $i(v0) | ~ aElementOf0(v0, % 70.53/10.75 | all_110_0) | aElementOf0(v0, all_110_1)) & ! [v0: $i] : ( ~ % 70.53/10.75 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 70.53/10.75 | = v0 & $i(v1) & aElementOf0(v1, all_110_1))) % 70.53/10.75 | % 70.53/10.75 | ALPHA: (18) implies: % 70.53/10.75 | (19) szDzizrdt0(xd) = all_110_2 % 70.53/10.75 | % 70.53/10.75 | BETA: splitting (2) gives: % 70.53/10.75 | % 70.53/10.75 | Case 1: % 70.53/10.75 | | % 70.53/10.75 | | (20) ~ aSet0(slcrc0) % 70.53/10.75 | | % 70.53/10.75 | | PRED_UNIFY: (1), (20) imply: % 70.53/10.75 | | (21) $false % 70.53/10.75 | | % 70.53/10.75 | | CLOSE: (21) is inconsistent. % 70.53/10.75 | | % 70.53/10.75 | Case 2: % 70.53/10.75 | | % 70.53/10.75 | | % 70.53/10.75 | | GROUND_INST: instantiating (7) with all_90_1, all_107_0, all_90_2, xd, % 70.53/10.75 | | simplifying with (12) gives: % 70.53/10.75 | | (22) all_107_0 = all_90_1 | ~ (sdtlbdtrb0(xd, all_90_2) = all_107_0) % 70.53/10.75 | | % 70.53/10.75 | | GROUND_INST: instantiating (6) with all_107_1, all_110_2, xd, simplifying % 70.53/10.75 | | with (16), (19) gives: % 70.53/10.75 | | (23) all_110_2 = all_107_1 % 70.53/10.75 | | % 70.53/10.75 | | GROUND_INST: instantiating (6) with all_90_2, all_110_2, xd, simplifying % 70.53/10.75 | | with (13), (19) gives: % 70.53/10.75 | | (24) all_110_2 = all_90_2 % 70.53/10.75 | | % 70.53/10.75 | | COMBINE_EQS: (23), (24) imply: % 70.53/10.75 | | (25) all_107_1 = all_90_2 % 70.53/10.75 | | % 70.53/10.75 | | SIMP: (25) implies: % 70.53/10.75 | | (26) all_107_1 = all_90_2 % 70.53/10.75 | | % 70.53/10.75 | | REDUCE: (15), (26) imply: % 70.53/10.75 | | (27) sdtlbdtrb0(xd, all_90_2) = all_107_0 % 70.53/10.75 | | % 70.53/10.75 | | BETA: splitting (22) gives: % 70.53/10.75 | | % 70.53/10.75 | | Case 1: % 70.53/10.75 | | | % 70.53/10.75 | | | (28) ~ (sdtlbdtrb0(xd, all_90_2) = all_107_0) % 70.53/10.75 | | | % 70.53/10.75 | | | PRED_UNIFY: (27), (28) imply: % 70.53/10.75 | | | (29) $false % 70.53/10.75 | | | % 70.53/10.75 | | | CLOSE: (29) is inconsistent. % 70.53/10.75 | | | % 70.53/10.75 | | Case 2: % 70.53/10.75 | | | % 70.53/10.75 | | | (30) all_107_0 = all_90_1 % 70.53/10.75 | | | % 70.53/10.75 | | | GROUND_INST: instantiating (17) with all_90_0, simplifying with (10), (11) % 70.53/10.75 | | | gives: % 70.53/10.75 | | | (31) ~ aElementOf0(all_90_0, all_107_0) % 70.53/10.75 | | | % 70.53/10.75 | | | REDUCE: (30), (31) imply: % 70.53/10.75 | | | (32) ~ aElementOf0(all_90_0, all_90_1) % 70.53/10.75 | | | % 70.53/10.75 | | | PRED_UNIFY: (9), (32) imply: % 70.53/10.75 | | | (33) $false % 70.53/10.75 | | | % 70.53/10.75 | | | CLOSE: (33) is inconsistent. % 70.53/10.75 | | | % 70.53/10.75 | | End of split % 70.53/10.75 | | % 70.53/10.75 | End of split % 70.53/10.75 | % 70.53/10.75 End of proof % 70.53/10.75 % SZS output end Proof for theBenchmark % 70.53/10.75 % 70.53/10.75 10138ms %------------------------------------------------------------------------------