%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM623+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 : n001.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 11:49:02 EDT 2023 % Result : Theorem 142.22s 19.59s % Output : Proof 142.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM623+3 : 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 : n001.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 10:17:28 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.47/1.65 Prover 1: Preprocessing ... % 6.92/1.68 Prover 4: Preprocessing ... % 6.92/1.70 Prover 3: Preprocessing ... % 6.92/1.70 Prover 6: Preprocessing ... % 6.92/1.70 Prover 0: Preprocessing ... % 6.92/1.70 Prover 2: Preprocessing ... % 6.92/1.70 Prover 5: Preprocessing ... % 20.01/3.57 Prover 3: Constructing countermodel ... % 20.01/3.58 Prover 1: Constructing countermodel ... % 20.77/3.62 Prover 6: Proving ... % 24.22/4.04 Prover 5: Proving ... % 45.61/6.89 Prover 4: Constructing countermodel ... % 50.04/7.44 Prover 2: Proving ... % 52.59/7.75 Prover 0: Proving ... % 99.96/13.96 Prover 5: stopped % 99.96/13.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 101.53/14.18 Prover 7: Preprocessing ... % 101.53/14.36 Prover 2: stopped % 101.53/14.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 104.24/14.56 Prover 8: Preprocessing ... % 106.58/14.86 Prover 7: Constructing countermodel ... % 107.33/14.96 Prover 8: Warning: ignoring some quantifiers % 107.33/15.02 Prover 8: Constructing countermodel ... % 115.06/15.96 Prover 1: stopped % 115.25/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.86/16.21 Prover 9: Preprocessing ... % 129.24/17.88 Prover 6: stopped % 129.24/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 131.22/18.14 Prover 10: Preprocessing ... % 133.16/18.49 Prover 10: Constructing countermodel ... % 135.64/18.72 Prover 9: Constructing countermodel ... % 142.22/19.56 Prover 10: Found proof (size 67) % 142.22/19.56 Prover 10: proved (1678ms) % 142.22/19.56 Prover 9: stopped % 142.22/19.56 Prover 7: stopped % 142.22/19.56 Prover 0: stopped % 142.22/19.56 Prover 8: stopped % 142.22/19.56 Prover 4: stopped % 142.22/19.59 Prover 3: stopped % 142.22/19.59 % 142.22/19.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 142.22/19.59 % 142.22/19.60 % SZS output start Proof for theBenchmark % 142.22/19.61 Assumptions after simplification: % 142.22/19.61 --------------------------------- % 142.22/19.61 % 142.22/19.61 (mCountNFin_01) % 142.22/19.62 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 142.22/19.62 % 142.22/19.62 (mDefEmp) % 142.22/19.62 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 142.22/19.62 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 142.22/19.62 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 142.22/19.62 % 142.22/19.62 (mMinMin) % 142.40/19.64 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 142.40/19.64 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ % 142.40/19.64 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) % 142.40/19.64 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2, % 142.40/19.64 v1)) % 142.40/19.64 % 142.40/19.64 (m__3671) % 142.40/19.65 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 142.40/19.65 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 142.40/19.65 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 142.40/19.65 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 142.40/19.65 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 142.40/19.65 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 142.40/19.65 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 142.40/19.65 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 142.40/19.65 % 142.40/19.65 (m__4660) % 142.40/19.65 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 142.40/19.65 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 142.40/19.65 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 142.40/19.65 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i] % 142.40/19.65 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3)))) % 142.40/19.65 % 142.40/19.65 (m__5093) % 142.40/19.65 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & % 142.40/19.65 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 142.40/19.65 aElementOf0(v1, xO))) % 142.40/19.65 % 142.40/19.65 (m__5106) % 142.40/19.65 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | % 142.40/19.65 ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0)) % 142.40/19.65 % 142.40/19.65 (m__5147) % 142.40/19.65 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : ( % 142.40/19.65 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0)) % 142.40/19.65 % 142.40/19.65 (m__5164) % 142.40/19.65 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 142.40/19.65 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 142.40/19.65 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 142.40/19.65 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 142.40/19.65 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 142.40/19.65 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 142.40/19.65 % 142.40/19.65 (m__5348) % 142.40/19.66 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & % 142.40/19.66 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 142.40/19.66 % 142.40/19.66 (m__5389) % 142.40/19.66 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 142.40/19.66 aElementOf0(xm, szNzAzT0) % 142.40/19.66 % 142.40/19.66 (m__5401) % 142.40/19.66 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & % 142.40/19.66 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 142.40/19.66 % 142.40/19.66 (m__5442) % 142.40/19.66 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.40/19.66 $i] : (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 142.40/19.66 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 142.40/19.66 aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 142.40/19.66 % 142.40/19.66 (m__5461) % 142.40/19.66 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 142.40/19.66 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! % 142.40/19.66 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 142.40/19.66 % 142.40/19.66 (m__5481) % 142.40/19.66 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) % 142.40/19.66 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0)) % 142.40/19.66 % 142.40/19.66 (function-axioms) % 142.60/19.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.60/19.67 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 142.60/19.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 142.60/19.67 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 142.60/19.67 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 142.60/19.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 142.60/19.67 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 142.60/19.67 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 142.60/19.67 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 142.60/19.67 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 142.60/19.67 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 142.60/19.67 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 142.60/19.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 142.60/19.67 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 142.60/19.67 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 142.60/19.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 142.60/19.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.60/19.67 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 142.60/19.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 142.60/19.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.60/19.67 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 142.60/19.67 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 142.60/19.67 v0)) % 142.60/19.67 % 142.60/19.67 Further assumptions not needed in the proof: % 142.60/19.67 -------------------------------------------- % 142.60/19.67 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 142.60/19.67 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 142.60/19.67 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 142.60/19.67 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 142.60/19.67 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 142.60/19.67 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 142.60/19.67 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 142.60/19.67 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 142.60/19.67 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 142.60/19.67 mZeroLess, mZeroNum, m__, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 142.60/19.67 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, % 142.60/19.67 m__4411, m__4618, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, % 142.60/19.67 m__5078, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, % 142.60/19.67 m__5321, m__5365 % 142.60/19.67 % 142.60/19.67 Those formulas are unsatisfiable: % 142.60/19.67 --------------------------------- % 142.60/19.67 % 142.60/19.67 Begin of proof % 142.60/19.67 | % 142.60/19.67 | ALPHA: (mDefEmp) implies: % 142.60/19.68 | (1) aSet0(slcrc0) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (mCountNFin_01) implies: % 142.60/19.68 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (mMinMin) implies: % 142.60/19.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = % 142.60/19.68 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0) % 142.60/19.68 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 142.60/19.68 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ % 142.60/19.68 | aElementOf0(v2, v1)) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__3671) implies: % 142.60/19.68 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 142.60/19.68 | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 142.60/19.68 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 142.60/19.68 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__4660) implies: % 142.60/19.68 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 142.60/19.68 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 142.60/19.68 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! % 142.60/19.68 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, % 142.60/19.68 | v3)))) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5093) implies: % 142.60/19.68 | (7) ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & aElementOf0(v0, xQ) & ! % 142.60/19.68 | [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, % 142.60/19.68 | xO))) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5106) implies: % 142.60/19.68 | (8) aSubsetOf0(xQ, szNzAzT0) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5147) implies: % 142.60/19.68 | (9) szmzizndt0(xQ) = xp % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5164) implies: % 142.60/19.68 | (10) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 142.60/19.68 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 142.60/19.68 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 142.60/19.68 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 142.60/19.68 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 142.60/19.68 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 142.60/19.68 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5348) implies: % 142.60/19.68 | (11) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) & % 142.60/19.68 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5389) implies: % 142.60/19.68 | (12) aElementOf0(xm, szNzAzT0) % 142.60/19.68 | (13) sdtlpdtrp0(xe, xm) = xx % 142.60/19.68 | % 142.60/19.68 | ALPHA: (m__5401) implies: % 142.60/19.69 | (14) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 142.60/19.69 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (m__5442) implies: % 142.60/19.69 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 142.60/19.69 | (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 142.60/19.69 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 142.60/19.69 | aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (m__5461) implies: % 142.60/19.69 | (16) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 142.60/19.69 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( % 142.60/19.69 | ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (m__5481) implies: % 142.60/19.69 | (17) $i(xQ) % 142.60/19.69 | (18) $i(xm) % 142.60/19.69 | (19) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ) % 142.60/19.69 | & aElementOf0(xp, v0)) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (function-axioms) implies: % 142.60/19.69 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.60/19.69 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 142.60/19.69 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.60/19.69 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (19) with fresh symbol all_86_0 gives: % 142.60/19.69 | (22) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & aElementOf0(xx, xQ) & % 142.60/19.69 | aElementOf0(xp, all_86_0) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (22) implies: % 142.60/19.69 | (23) aElementOf0(xp, all_86_0) % 142.60/19.69 | (24) sdtlpdtrp0(xN, xm) = all_86_0 % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (14) with fresh symbol all_88_0 gives: % 142.60/19.69 | (25) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & ! [v0: $i] : ( ~ % 142.60/19.69 | $i(v0) | ~ aElementOf0(v0, all_88_0) | sdtlseqdt0(xx, v0)) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (25) implies: % 142.60/19.69 | (26) sdtlpdtrp0(xN, xm) = all_88_0 % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (11) with fresh symbol all_91_0 gives: % 142.60/19.69 | (27) ~ (all_91_0 = xx) & szmzizndt0(xQ) = all_91_0 & $i(all_91_0) & % 142.60/19.69 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (27) implies: % 142.60/19.69 | (28) ~ (all_91_0 = xx) % 142.60/19.69 | (29) aElementOf0(xx, xQ) % 142.60/19.69 | (30) szmzizndt0(xQ) = all_91_0 % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (7) with fresh symbol all_93_0 gives: % 142.60/19.69 | (31) ~ (xQ = slcrc0) & $i(all_93_0) & aElementOf0(all_93_0, xQ) & ! [v0: % 142.60/19.69 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (31) implies: % 142.60/19.69 | (32) ~ (xQ = slcrc0) % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (16) with fresh symbols all_101_0, all_101_1 gives: % 142.60/19.69 | (33) sdtlpdtrp0(xN, xm) = all_101_0 & sdtlpdtrp0(xN, xn) = all_101_1 & % 142.60/19.69 | $i(all_101_0) & $i(all_101_1) & aSubsetOf0(all_101_1, all_101_0) & ! % 142.60/19.69 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_101_1) | % 142.60/19.69 | aElementOf0(v0, all_101_0)) % 142.60/19.69 | % 142.60/19.69 | ALPHA: (33) implies: % 142.60/19.69 | (34) sdtlpdtrp0(xN, xm) = all_101_0 % 142.60/19.69 | % 142.60/19.69 | DELTA: instantiating (15) with fresh symbols all_109_0, all_109_1, all_109_2, % 142.60/19.69 | all_109_3 gives: % 142.60/19.70 | (35) sdtlpdtrp0(xN, all_109_2) = all_109_1 & sdtlpdtrp0(xN, xm) = all_109_3 % 142.60/19.70 | & szszuzczcdt0(xn) = all_109_2 & $i(all_109_0) & $i(all_109_1) & % 142.60/19.70 | $i(all_109_2) & $i(all_109_3) & aElementOf0(all_109_0, all_109_3) & ~ % 142.60/19.70 | aSubsetOf0(all_109_3, all_109_1) & ~ aElementOf0(all_109_0, % 142.60/19.70 | all_109_1) % 142.60/19.70 | % 142.60/19.70 | ALPHA: (35) implies: % 142.60/19.70 | (36) sdtlpdtrp0(xN, xm) = all_109_3 % 142.60/19.70 | % 142.60/19.70 | DELTA: instantiating (10) with fresh symbol all_113_0 gives: % 142.60/19.70 | (37) szmzizndt0(xQ) = all_113_0 & sdtmndt0(xQ, all_113_0) = xP & % 142.60/19.70 | $i(all_113_0) & aSet0(xP) & ~ aElementOf0(all_113_0, xP) & ! [v0: % 142.60/19.70 | any] : (v0 = all_113_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ % 142.60/19.70 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 142.60/19.70 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ % 142.60/19.70 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ % 142.60/19.70 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_113_0, v0)) % 142.60/19.70 | % 142.60/19.70 | ALPHA: (37) implies: % 142.60/19.70 | (38) szmzizndt0(xQ) = all_113_0 % 142.60/19.70 | % 142.60/19.70 | BETA: splitting (2) gives: % 142.60/19.70 | % 142.60/19.70 | Case 1: % 142.60/19.70 | | % 142.60/19.70 | | (39) ~ aSet0(slcrc0) % 142.60/19.70 | | % 142.60/19.70 | | PRED_UNIFY: (1), (39) imply: % 142.60/19.70 | | (40) $false % 142.60/19.70 | | % 142.60/19.70 | | CLOSE: (40) is inconsistent. % 142.60/19.70 | | % 142.60/19.70 | Case 2: % 142.60/19.70 | | % 142.60/19.70 | | (41) ~ isCountable0(slcrc0) % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (20) with all_91_0, all_113_0, xQ, simplifying % 142.60/19.70 | | with (30), (38) gives: % 142.60/19.70 | | (42) all_113_0 = all_91_0 % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (20) with xp, all_113_0, xQ, simplifying with % 142.60/19.70 | | (9), (38) gives: % 142.60/19.70 | | (43) all_113_0 = xp % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (21) with all_88_0, all_101_0, xm, xN, % 142.60/19.70 | | simplifying with (26), (34) gives: % 142.60/19.70 | | (44) all_101_0 = all_88_0 % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (21) with all_101_0, all_109_3, xm, xN, % 142.60/19.70 | | simplifying with (34), (36) gives: % 142.60/19.70 | | (45) all_109_3 = all_101_0 % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (21) with all_86_0, all_109_3, xm, xN, % 142.60/19.70 | | simplifying with (24), (36) gives: % 142.60/19.70 | | (46) all_109_3 = all_86_0 % 142.60/19.70 | | % 142.60/19.70 | | COMBINE_EQS: (42), (43) imply: % 142.60/19.70 | | (47) all_91_0 = xp % 142.60/19.70 | | % 142.60/19.70 | | SIMP: (47) implies: % 142.60/19.70 | | (48) all_91_0 = xp % 142.60/19.70 | | % 142.60/19.70 | | COMBINE_EQS: (45), (46) imply: % 142.60/19.70 | | (49) all_101_0 = all_86_0 % 142.60/19.70 | | % 142.60/19.70 | | SIMP: (49) implies: % 142.60/19.70 | | (50) all_101_0 = all_86_0 % 142.60/19.70 | | % 142.60/19.70 | | COMBINE_EQS: (44), (50) imply: % 142.60/19.70 | | (51) all_88_0 = all_86_0 % 142.60/19.70 | | % 142.60/19.70 | | SIMP: (51) implies: % 142.60/19.70 | | (52) all_88_0 = all_86_0 % 142.60/19.70 | | % 142.60/19.70 | | REDUCE: (28), (48) imply: % 142.60/19.70 | | (53) ~ (xx = xp) % 142.60/19.70 | | % 142.60/19.70 | | SIMP: (53) implies: % 142.60/19.70 | | (54) ~ (xx = xp) % 142.60/19.70 | | % 142.60/19.70 | | GROUND_INST: instantiating (5) with xm, all_86_0, simplifying with (12), % 142.60/19.70 | | (18), (24) gives: % 142.60/19.70 | | (55) aSubsetOf0(all_86_0, szNzAzT0) % 142.60/19.70 | | % 142.60/19.71 | | GROUND_INST: instantiating (4) with xm, all_86_0, simplifying with (12), % 142.60/19.71 | | (18), (24) gives: % 142.60/19.71 | | (56) isCountable0(all_86_0) % 142.60/19.71 | | % 142.60/19.71 | | GROUND_INST: instantiating (6) with xm, xx, simplifying with (12), (13), % 142.60/19.71 | | (18) gives: % 142.60/19.71 | | (57) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & % 142.60/19.71 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) | % 142.60/19.71 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 142.60/19.71 | | % 142.60/19.71 | | DELTA: instantiating (57) with fresh symbol all_157_0 gives: % 142.60/19.71 | | (58) sdtlpdtrp0(xN, xm) = all_157_0 & szmzizndt0(all_157_0) = xx & % 142.60/19.71 | | $i(all_157_0) & $i(xx) & aElementOf0(xx, all_157_0) & ! [v0: $i] : % 142.60/19.71 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_157_0) | sdtlseqdt0(xx, v0)) % 142.60/19.71 | | % 142.60/19.71 | | ALPHA: (58) implies: % 142.60/19.71 | | (59) $i(all_157_0) % 142.60/19.71 | | (60) szmzizndt0(all_157_0) = xx % 142.60/19.71 | | (61) sdtlpdtrp0(xN, xm) = all_157_0 % 142.60/19.71 | | % 142.60/19.71 | | GROUND_INST: instantiating (21) with all_86_0, all_157_0, xm, xN, % 142.60/19.71 | | simplifying with (24), (61) gives: % 142.60/19.71 | | (62) all_157_0 = all_86_0 % 142.60/19.71 | | % 142.60/19.71 | | REDUCE: (60), (62) imply: % 142.60/19.71 | | (63) szmzizndt0(all_86_0) = xx % 142.60/19.71 | | % 142.60/19.71 | | REDUCE: (59), (62) imply: % 142.60/19.71 | | (64) $i(all_86_0) % 142.60/19.71 | | % 142.60/19.71 | | GROUND_INST: instantiating (3) with all_86_0, xQ, xx, xp, simplifying with % 142.60/19.71 | | (8), (9), (17), (23), (29), (55), (63), (64) gives: % 142.60/19.71 | | (65) all_86_0 = slcrc0 | xx = xp | xQ = slcrc0 % 142.60/19.71 | | % 142.60/19.71 | | BETA: splitting (65) gives: % 142.60/19.71 | | % 142.60/19.71 | | Case 1: % 142.60/19.71 | | | % 142.60/19.71 | | | (66) all_86_0 = slcrc0 % 142.60/19.71 | | | % 142.60/19.71 | | | REDUCE: (56), (66) imply: % 142.60/19.71 | | | (67) isCountable0(slcrc0) % 142.60/19.71 | | | % 142.60/19.71 | | | PRED_UNIFY: (41), (67) imply: % 142.60/19.71 | | | (68) $false % 142.60/19.71 | | | % 142.60/19.71 | | | CLOSE: (68) is inconsistent. % 142.60/19.71 | | | % 142.60/19.71 | | Case 2: % 142.60/19.71 | | | % 142.60/19.71 | | | (69) xx = xp | xQ = slcrc0 % 142.60/19.71 | | | % 142.60/19.71 | | | BETA: splitting (69) gives: % 142.60/19.71 | | | % 142.60/19.71 | | | Case 1: % 142.60/19.71 | | | | % 142.60/19.71 | | | | (70) xQ = slcrc0 % 142.60/19.71 | | | | % 142.60/19.71 | | | | REDUCE: (32), (70) imply: % 142.60/19.71 | | | | (71) $false % 142.60/19.71 | | | | % 142.60/19.71 | | | | CLOSE: (71) is inconsistent. % 142.60/19.71 | | | | % 142.60/19.71 | | | Case 2: % 142.60/19.71 | | | | % 142.60/19.71 | | | | (72) xx = xp % 142.60/19.71 | | | | % 142.60/19.71 | | | | REDUCE: (54), (72) imply: % 142.60/19.71 | | | | (73) $false % 142.60/19.71 | | | | % 142.60/19.71 | | | | CLOSE: (73) is inconsistent. % 142.60/19.71 | | | | % 142.60/19.71 | | | End of split % 142.60/19.71 | | | % 142.60/19.71 | | End of split % 142.60/19.71 | | % 142.60/19.71 | End of split % 142.60/19.71 | % 142.60/19.71 End of proof % 142.60/19.71 % SZS output end Proof for theBenchmark % 142.60/19.71 % 142.60/19.71 19114ms %------------------------------------------------------------------------------