%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM625+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 : n002.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 19.84s 3.49s % Output : Proof 45.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM625+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n002.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Aug 25 14:16:47 EDT 2023 % 0.11/0.33 % CPUTime : % 0.17/0.58 ________ _____ % 0.17/0.58 ___ __ \_________(_)________________________________ % 0.17/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.58 % 0.17/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.58 (2023-06-19) % 0.17/0.58 % 0.17/0.58 (c) Philipp Rümmer, 2009-2023 % 0.17/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.58 Amanda Stjerna. % 0.17/0.58 Free software under BSD-3-Clause. % 0.17/0.58 % 0.17/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.58 % 0.17/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.59 Running up to 7 provers in parallel. % 0.17/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.17/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 7.59/1.84 Prover 1: Preprocessing ... % 7.59/1.84 Prover 4: Preprocessing ... % 7.59/1.89 Prover 2: Preprocessing ... % 7.59/1.89 Prover 3: Preprocessing ... % 7.59/1.89 Prover 6: Preprocessing ... % 7.59/1.89 Prover 0: Preprocessing ... % 7.59/1.90 Prover 5: Preprocessing ... % 18.62/3.44 Prover 3: Constructing countermodel ... % 19.84/3.48 Prover 3: proved (2874ms) % 19.84/3.48 % 19.84/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.84/3.49 % 19.84/3.49 Prover 2: stopped % 19.84/3.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.84/3.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.87/3.64 Prover 6: Constructing countermodel ... % 20.87/3.64 Prover 6: stopped % 21.35/3.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.27/3.82 Prover 7: Preprocessing ... % 22.56/3.88 Prover 8: Preprocessing ... % 23.13/3.97 Prover 0: stopped % 23.13/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.13/4.08 Prover 10: Preprocessing ... % 27.36/4.49 Prover 11: Preprocessing ... % 28.73/4.81 Prover 1: Constructing countermodel ... % 29.90/4.89 Prover 5: Constructing countermodel ... % 29.90/4.89 Prover 5: stopped % 30.44/4.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 31.55/5.08 Prover 8: Warning: ignoring some quantifiers % 32.28/5.15 Prover 8: Constructing countermodel ... % 32.28/5.18 Prover 13: Preprocessing ... % 34.78/5.57 Prover 1: Found proof (size 16) % 34.78/5.57 Prover 1: proved (4961ms) % 34.78/5.57 Prover 11: stopped % 34.78/5.57 Prover 8: stopped % 34.78/5.57 Prover 13: stopped % 36.62/5.75 Prover 10: Constructing countermodel ... % 36.62/5.77 Prover 10: stopped % 37.18/5.87 Prover 7: Constructing countermodel ... % 37.18/5.89 Prover 7: stopped % 45.65/7.94 Prover 4: Constructing countermodel ... % 45.91/8.03 Prover 4: stopped % 45.91/8.03 % 45.91/8.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 45.91/8.03 % 45.91/8.03 % SZS output start Proof for theBenchmark % 45.91/8.04 Assumptions after simplification: % 45.91/8.04 --------------------------------- % 45.91/8.04 % 45.91/8.04 (m__5147) % 45.91/8.07 szmzizndt0(xQ) = xp & aElementOf0(xp, xQ) = 0 & $i(xp) & $i(xQ) & ! [v0: $i] % 45.91/8.07 : ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(xp, v0) = v1) | ~ $i(v0) | ? [v2: % 45.91/8.07 int] : ( ~ (v2 = 0) & aElementOf0(v0, xQ) = v2)) % 45.91/8.07 % 45.91/8.07 (m__5164) % 45.91/8.08 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 45.91/8.08 aSet0(xP) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 45.91/8.08 (aElementOf0(v1, xP) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 45.91/8.08 (aElement0(v1) = v3 & aElementOf0(v1, xQ) = v4 & ( ~ (v4 = 0) | ~ (v3 = % 45.91/8.08 0)))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, % 45.91/8.08 v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, % 45.91/8.08 xQ) = v3)) & ! [v1: $i] : ( ~ (aElementOf0(v1, xP) = 0) | ~ $i(v1) | % 45.91/8.08 ( ~ (v1 = v0) & aElement0(v1) = 0 & aElementOf0(v1, xQ) = 0))) % 45.91/8.08 % 45.91/8.08 (m__5348) % 45.91/8.08 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & % 45.91/8.08 aElement0(xx) = 0 & aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 & % 45.91/8.08 $i(v0)) % 45.91/8.08 % 45.91/8.08 (m__5496) % 45.91/8.08 xx = xp & $i(xp) % 45.91/8.08 % 45.91/8.08 (function-axioms) % 45.91/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.91/8.10 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 45.91/8.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 45.91/8.10 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 45.91/8.10 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 45.91/8.10 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 45.91/8.10 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 45.91/8.10 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 45.91/8.10 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.91/8.10 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: % 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.91/8.10 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 45.91/8.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.91/8.10 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 45.91/8.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 45.91/8.10 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.91/8.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.91/8.10 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.91/8.10 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 45.91/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 45.91/8.10 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.91/8.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~ % 45.91/8.10 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 45.91/8.10 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 45.91/8.10 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 45.91/8.10 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 45.91/8.10 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 45.91/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 45.91/8.10 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 45.91/8.10 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 45.91/8.10 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 45.91/8.10 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 45.91/8.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 45.91/8.10 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 45.91/8.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 45.91/8.10 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 45.91/8.10 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 45.91/8.10 ~ (aElement0(v2) = v0)) % 45.91/8.10 % 45.91/8.10 Further assumptions not needed in the proof: % 45.91/8.10 -------------------------------------------- % 45.91/8.10 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 45.91/8.10 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 45.91/8.10 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 45.91/8.10 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 45.91/8.10 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 45.91/8.10 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 45.91/8.10 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 45.91/8.10 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 45.91/8.10 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 45.91/8.10 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__, m__3291, m__3398, % 45.91/8.10 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 45.91/8.10 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, % 45.91/8.10 m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, % 45.91/8.10 m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, m__5321, % 45.91/8.10 m__5365, m__5389, m__5401, m__5442, m__5461, m__5481 % 45.91/8.10 % 45.91/8.10 Those formulas are unsatisfiable: % 45.91/8.10 --------------------------------- % 45.91/8.10 % 45.91/8.10 Begin of proof % 45.91/8.10 | % 45.91/8.10 | ALPHA: (m__5147) implies: % 45.91/8.10 | (1) szmzizndt0(xQ) = xp % 45.91/8.10 | % 45.91/8.10 | ALPHA: (m__5164) implies: % 45.91/8.11 | (2) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & aSet0(xP) % 45.91/8.11 | = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 45.91/8.11 | (aElementOf0(v1, xP) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 45.91/8.11 | any] : (aElement0(v1) = v3 & aElementOf0(v1, xQ) = v4 & ( ~ (v4 = % 45.91/8.11 | 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 45.91/8.11 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 45.91/8.11 | 0) & aElementOf0(v1, xQ) = v3)) & ! [v1: $i] : ( ~ % 45.91/8.11 | (aElementOf0(v1, xP) = 0) | ~ $i(v1) | ( ~ (v1 = v0) & % 45.91/8.11 | aElement0(v1) = 0 & aElementOf0(v1, xQ) = 0))) % 45.91/8.11 | % 45.91/8.11 | ALPHA: (m__5348) implies: % 45.91/8.11 | (3) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & aElement0(xx) = 0 & % 45.91/8.11 | aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 & $i(v0)) % 45.91/8.11 | % 45.91/8.11 | ALPHA: (m__5496) implies: % 45.91/8.11 | (4) xx = xp % 45.91/8.11 | % 45.91/8.11 | ALPHA: (function-axioms) implies: % 45.91/8.11 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) % 45.91/8.11 | = v1) | ~ (szmzizndt0(v2) = v0)) % 45.91/8.11 | % 45.91/8.11 | DELTA: instantiating (3) with fresh symbol all_94_0 gives: % 45.91/8.11 | (6) ~ (all_94_0 = xx) & szmzizndt0(xQ) = all_94_0 & aElement0(xx) = 0 & % 45.91/8.11 | aElementOf0(xx, xP) = 0 & aElementOf0(xx, xQ) = 0 & $i(all_94_0) % 45.91/8.11 | % 45.91/8.11 | ALPHA: (6) implies: % 45.91/8.11 | (7) ~ (all_94_0 = xx) % 45.91/8.11 | (8) szmzizndt0(xQ) = all_94_0 % 45.91/8.12 | % 45.91/8.12 | DELTA: instantiating (2) with fresh symbol all_122_0 gives: % 45.91/8.12 | (9) szmzizndt0(xQ) = all_122_0 & sdtmndt0(xQ, all_122_0) = xP & aSet0(xP) = % 45.91/8.12 | 0 & $i(all_122_0) & ! [v0: any] : ! [v1: int] : (v1 = 0 | v0 = % 45.91/8.12 | all_122_0 | ~ (aElementOf0(v0, xP) = v1) | ~ $i(v0) | ? [v2: any] % 45.91/8.12 | : ? [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0, xQ) = v3 & ( ~ % 45.91/8.12 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 45.91/8.12 | | ~ (sdtlseqdt0(all_122_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( % 45.91/8.12 | ~ (v2 = 0) & aElementOf0(v0, xQ) = v2)) & ! [v0: $i] : ( ~ % 45.91/8.12 | (aElementOf0(v0, xP) = 0) | ~ $i(v0) | ( ~ (v0 = all_122_0) & % 45.91/8.12 | aElement0(v0) = 0 & aElementOf0(v0, xQ) = 0)) % 45.91/8.12 | % 45.91/8.12 | ALPHA: (9) implies: % 45.91/8.12 | (10) szmzizndt0(xQ) = all_122_0 % 45.91/8.12 | % 45.91/8.12 | REDUCE: (4), (7) imply: % 45.91/8.12 | (11) ~ (all_94_0 = xp) % 45.91/8.12 | % 45.91/8.12 | GROUND_INST: instantiating (5) with all_94_0, all_122_0, xQ, simplifying with % 45.91/8.12 | (8), (10) gives: % 45.91/8.12 | (12) all_122_0 = all_94_0 % 45.91/8.12 | % 45.91/8.12 | GROUND_INST: instantiating (5) with xp, all_122_0, xQ, simplifying with (1), % 45.91/8.12 | (10) gives: % 45.91/8.12 | (13) all_122_0 = xp % 45.91/8.12 | % 45.91/8.12 | COMBINE_EQS: (12), (13) imply: % 45.91/8.12 | (14) all_94_0 = xp % 45.91/8.12 | % 45.91/8.12 | SIMP: (14) implies: % 45.91/8.12 | (15) all_94_0 = xp % 45.91/8.12 | % 45.91/8.12 | REDUCE: (11), (15) imply: % 45.91/8.12 | (16) $false % 45.91/8.12 | % 45.91/8.12 | CLOSE: (16) is inconsistent. % 45.91/8.12 | % 45.91/8.12 End of proof % 45.91/8.12 % SZS output end Proof for theBenchmark % 45.91/8.12 % 45.91/8.12 7542ms %------------------------------------------------------------------------------