%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM624+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 : n009.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 144.05s 19.68s % Output : Proof 144.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM624+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 10:05:06 EDT 2023 % 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.65 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 6.28/1.61 Prover 4: Preprocessing ... % 6.28/1.61 Prover 1: Preprocessing ... % 7.01/1.66 Prover 5: Preprocessing ... % 7.01/1.66 Prover 0: Preprocessing ... % 7.01/1.66 Prover 6: Preprocessing ... % 7.01/1.66 Prover 2: Preprocessing ... % 7.01/1.66 Prover 3: Preprocessing ... % 20.19/3.42 Prover 1: Constructing countermodel ... % 20.27/3.43 Prover 3: Constructing countermodel ... % 20.27/3.50 Prover 6: Proving ... % 23.69/3.96 Prover 5: Proving ... % 45.22/6.69 Prover 4: Constructing countermodel ... % 51.31/7.56 Prover 2: Proving ... % 53.52/7.87 Prover 0: Proving ... % 100.32/13.99 Prover 5: stopped % 100.32/13.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 102.50/14.25 Prover 7: Preprocessing ... % 105.03/14.58 Prover 2: stopped % 105.03/14.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 106.82/14.77 Prover 8: Preprocessing ... % 108.66/15.05 Prover 7: Constructing countermodel ... % 109.16/15.14 Prover 8: Warning: ignoring some quantifiers % 109.16/15.15 Prover 8: Constructing countermodel ... % 116.27/16.01 Prover 1: stopped % 116.27/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 118.03/16.22 Prover 9: Preprocessing ... % 130.68/17.90 Prover 6: stopped % 130.68/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.07/18.14 Prover 10: Preprocessing ... % 133.57/18.31 Prover 9: Constructing countermodel ... % 136.20/18.65 Prover 10: Constructing countermodel ... % 143.41/19.62 Prover 10: Found proof (size 73) % 143.41/19.63 Prover 10: proved (1719ms) % 143.41/19.63 Prover 9: stopped % 143.41/19.63 Prover 8: stopped % 143.41/19.63 Prover 7: stopped % 143.41/19.64 Prover 3: stopped % 143.41/19.64 Prover 4: stopped % 144.05/19.68 Prover 0: stopped % 144.05/19.68 % 144.05/19.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 144.05/19.68 % 144.21/19.69 % SZS output start Proof for theBenchmark % 144.21/19.69 Assumptions after simplification: % 144.21/19.69 --------------------------------- % 144.21/19.69 % 144.21/19.69 (mCountNFin_01) % 144.21/19.70 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 144.21/19.70 % 144.21/19.70 (mDefEmp) % 144.21/19.70 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 144.21/19.70 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 144.21/19.70 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 144.21/19.70 % 144.21/19.70 (mMinMin) % 144.21/19.73 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 144.21/19.73 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ % 144.21/19.73 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) % 144.21/19.73 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2, % 144.21/19.73 v1)) % 144.21/19.73 % 144.21/19.73 (m__3671) % 144.21/19.73 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 144.21/19.73 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 144.21/19.73 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 144.21/19.73 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 144.21/19.73 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 144.21/19.73 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 144.21/19.73 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 144.21/19.73 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 144.41/19.73 % 144.41/19.73 (m__4660) % 144.41/19.73 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 144.41/19.73 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 144.41/19.73 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 144.41/19.73 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i] % 144.41/19.73 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3)))) % 144.41/19.73 % 144.41/19.73 (m__5093) % 144.41/19.74 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & % 144.41/19.74 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 144.41/19.74 aElementOf0(v1, xO))) % 144.41/19.74 % 144.41/19.74 (m__5106) % 144.41/19.74 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | % 144.41/19.74 ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0)) % 144.41/19.74 % 144.41/19.74 (m__5147) % 144.41/19.74 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : ( % 144.41/19.74 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0)) % 144.41/19.74 % 144.41/19.74 (m__5164) % 144.45/19.74 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 144.45/19.74 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 144.45/19.74 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 144.45/19.74 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 144.45/19.74 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 144.45/19.74 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 144.45/19.74 % 144.45/19.74 (m__5348) % 144.45/19.74 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & % 144.45/19.74 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 144.45/19.74 % 144.45/19.74 (m__5389) % 144.45/19.74 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 144.45/19.74 aElementOf0(xm, szNzAzT0) % 144.45/19.74 % 144.45/19.74 (m__5401) % 144.45/19.74 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & % 144.45/19.74 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 144.45/19.74 % 144.45/19.74 (m__5442) % 144.45/19.75 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 144.45/19.75 $i] : (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 144.45/19.75 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 144.45/19.75 aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 144.45/19.75 % 144.45/19.75 (m__5461) % 144.45/19.75 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 144.45/19.75 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! % 144.45/19.75 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 144.45/19.75 % 144.45/19.75 (m__5481) % 144.45/19.75 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) % 144.45/19.75 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0)) % 144.45/19.75 % 144.45/19.75 (m__5518) % 144.45/19.75 $i(xm) & $i(xQ) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 144.45/19.75 $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, % 144.45/19.75 xQ) & aElementOf0(v1, v0) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, % 144.45/19.75 v0) | aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 144.45/19.75 aElementOf0(v3, xQ) | aElementOf0(v3, szNzAzT0))) % 144.45/19.75 % 144.45/19.75 (function-axioms) % 144.45/19.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 144.45/19.76 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 144.45/19.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 144.45/19.76 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 144.45/19.76 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 144.45/19.76 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 144.45/19.76 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 144.45/19.76 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 144.45/19.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 144.45/19.76 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 144.45/19.76 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 144.45/19.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 144.45/19.76 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 144.45/19.76 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 144.45/19.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 144.45/19.76 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 144.45/19.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 144.45/19.76 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 144.45/19.76 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 144.45/19.76 v0)) % 144.45/19.76 % 144.45/19.76 Further assumptions not needed in the proof: % 144.45/19.76 -------------------------------------------- % 144.45/19.76 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 144.45/19.76 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 144.45/19.76 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 144.45/19.76 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 144.45/19.76 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 144.45/19.76 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 144.45/19.76 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 144.45/19.76 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 144.45/19.76 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 144.45/19.76 mZeroLess, mZeroNum, m__, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 144.45/19.76 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, % 144.45/19.76 m__4411, m__4618, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, % 144.45/19.76 m__5078, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, % 144.45/19.76 m__5321, m__5365 % 144.45/19.76 % 144.45/19.76 Those formulas are unsatisfiable: % 144.45/19.76 --------------------------------- % 144.45/19.76 % 144.45/19.76 Begin of proof % 144.45/19.76 | % 144.45/19.76 | ALPHA: (mDefEmp) implies: % 144.45/19.77 | (1) aSet0(slcrc0) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (mCountNFin_01) implies: % 144.45/19.77 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (mMinMin) implies: % 144.45/19.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = % 144.45/19.77 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0) % 144.45/19.77 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 144.45/19.77 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ % 144.45/19.77 | aElementOf0(v2, v1)) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__3671) implies: % 144.45/19.77 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 144.45/19.77 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__4660) implies: % 144.45/19.77 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 144.45/19.77 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! % 144.45/19.77 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, % 144.45/19.77 | v3)))) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5093) implies: % 144.45/19.77 | (7) ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & aElementOf0(v0, xQ) & ! % 144.45/19.77 | [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, % 144.45/19.77 | xO))) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5106) implies: % 144.45/19.77 | (8) aSubsetOf0(xQ, szNzAzT0) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5147) implies: % 144.45/19.77 | (9) szmzizndt0(xQ) = xp % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5164) implies: % 144.45/19.77 | (10) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 144.45/19.77 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 144.45/19.77 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 144.45/19.77 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 144.45/19.77 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 144.45/19.77 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 144.45/19.77 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5348) implies: % 144.45/19.77 | (11) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) & % 144.45/19.77 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5389) implies: % 144.45/19.77 | (12) aElementOf0(xm, szNzAzT0) % 144.45/19.77 | (13) sdtlpdtrp0(xe, xm) = xx % 144.45/19.77 | % 144.45/19.77 | ALPHA: (m__5401) implies: % 144.45/19.78 | (14) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 144.45/19.78 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (m__5442) implies: % 144.45/19.78 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 144.45/19.78 | (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 144.45/19.78 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 144.45/19.78 | aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (m__5461) implies: % 144.45/19.78 | (16) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 144.45/19.78 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( % 144.45/19.78 | ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (m__5481) implies: % 144.45/19.78 | (17) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ) % 144.45/19.78 | & aElementOf0(xp, v0)) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (m__5518) implies: % 144.45/19.78 | (18) $i(xQ) % 144.45/19.78 | (19) $i(xm) % 144.45/19.78 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xm) = v0 & % 144.45/19.78 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, xQ) & aElementOf0(v1, v0) % 144.45/19.78 | & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | % 144.45/19.78 | aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 144.45/19.78 | aElementOf0(v3, xQ) | aElementOf0(v3, szNzAzT0))) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (function-axioms) implies: % 144.45/19.78 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 144.45/19.78 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 144.45/19.78 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 144.45/19.78 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 144.45/19.78 | % 144.45/19.78 | DELTA: instantiating (17) with fresh symbol all_86_0 gives: % 144.45/19.78 | (23) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & aElementOf0(xx, xQ) & % 144.45/19.78 | aElementOf0(xp, all_86_0) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (23) implies: % 144.45/19.78 | (24) aElementOf0(xp, all_86_0) % 144.45/19.78 | (25) sdtlpdtrp0(xN, xm) = all_86_0 % 144.45/19.78 | % 144.45/19.78 | DELTA: instantiating (14) with fresh symbol all_88_0 gives: % 144.45/19.78 | (26) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & ! [v0: $i] : ( ~ % 144.45/19.78 | $i(v0) | ~ aElementOf0(v0, all_88_0) | sdtlseqdt0(xx, v0)) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (26) implies: % 144.45/19.78 | (27) sdtlpdtrp0(xN, xm) = all_88_0 % 144.45/19.78 | % 144.45/19.78 | DELTA: instantiating (11) with fresh symbol all_91_0 gives: % 144.45/19.78 | (28) ~ (all_91_0 = xx) & szmzizndt0(xQ) = all_91_0 & $i(all_91_0) & % 144.45/19.78 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx) % 144.45/19.78 | % 144.45/19.78 | ALPHA: (28) implies: % 144.45/19.78 | (29) ~ (all_91_0 = xx) % 144.45/19.78 | (30) aElementOf0(xx, xQ) % 144.45/19.78 | (31) szmzizndt0(xQ) = all_91_0 % 144.45/19.78 | % 144.45/19.78 | DELTA: instantiating (7) with fresh symbol all_93_0 gives: % 144.45/19.78 | (32) ~ (xQ = slcrc0) & $i(all_93_0) & aElementOf0(all_93_0, xQ) & ! [v0: % 144.45/19.78 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 144.45/19.79 | % 144.45/19.79 | ALPHA: (32) implies: % 144.45/19.79 | (33) ~ (xQ = slcrc0) % 144.45/19.79 | % 144.45/19.79 | DELTA: instantiating (16) with fresh symbols all_103_0, all_103_1 gives: % 144.45/19.79 | (34) sdtlpdtrp0(xN, xm) = all_103_0 & sdtlpdtrp0(xN, xn) = all_103_1 & % 144.45/19.79 | $i(all_103_0) & $i(all_103_1) & aSubsetOf0(all_103_1, all_103_0) & ! % 144.45/19.79 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_103_1) | % 144.45/19.79 | aElementOf0(v0, all_103_0)) % 144.45/19.79 | % 144.45/19.79 | ALPHA: (34) implies: % 144.45/19.79 | (35) sdtlpdtrp0(xN, xm) = all_103_0 % 144.45/19.79 | % 144.45/19.79 | DELTA: instantiating (15) with fresh symbols all_109_0, all_109_1, all_109_2, % 144.45/19.79 | all_109_3 gives: % 144.45/19.79 | (36) sdtlpdtrp0(xN, all_109_2) = all_109_1 & sdtlpdtrp0(xN, xm) = all_109_3 % 144.45/19.79 | & szszuzczcdt0(xn) = all_109_2 & $i(all_109_0) & $i(all_109_1) & % 144.45/19.79 | $i(all_109_2) & $i(all_109_3) & aElementOf0(all_109_0, all_109_3) & ~ % 144.45/19.79 | aSubsetOf0(all_109_3, all_109_1) & ~ aElementOf0(all_109_0, % 144.45/19.79 | all_109_1) % 144.45/19.79 | % 144.45/19.79 | ALPHA: (36) implies: % 144.45/19.79 | (37) sdtlpdtrp0(xN, xm) = all_109_3 % 144.45/19.79 | % 144.45/19.79 | DELTA: instantiating (20) with fresh symbols all_113_0, all_113_1, all_113_2 % 144.45/19.79 | gives: % 144.45/19.79 | (38) sdtlpdtrp0(xN, xm) = all_113_2 & $i(all_113_0) & $i(all_113_1) & % 144.45/19.79 | $i(all_113_2) & aElementOf0(all_113_0, xQ) & aElementOf0(all_113_1, % 144.45/19.79 | all_113_2) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 144.45/19.79 | all_113_2) | aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ( ~ $i(v0) % 144.45/19.79 | | ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0)) % 144.45/19.79 | % 144.45/19.79 | ALPHA: (38) implies: % 144.45/19.79 | (39) sdtlpdtrp0(xN, xm) = all_113_2 % 144.45/19.79 | % 144.45/19.79 | DELTA: instantiating (10) with fresh symbol all_116_0 gives: % 144.45/19.79 | (40) szmzizndt0(xQ) = all_116_0 & sdtmndt0(xQ, all_116_0) = xP & % 144.45/19.79 | $i(all_116_0) & aSet0(xP) & ~ aElementOf0(all_116_0, xP) & ! [v0: % 144.45/19.79 | any] : (v0 = all_116_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ % 144.45/19.79 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 144.45/19.79 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ % 144.45/19.79 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ % 144.45/19.79 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_116_0, v0)) % 144.45/19.79 | % 144.45/19.79 | ALPHA: (40) implies: % 144.45/19.79 | (41) szmzizndt0(xQ) = all_116_0 % 144.45/19.79 | % 144.45/19.79 | BETA: splitting (2) gives: % 144.45/19.79 | % 144.45/19.79 | Case 1: % 144.45/19.79 | | % 144.45/19.79 | | (42) ~ aSet0(slcrc0) % 144.45/19.79 | | % 144.45/19.79 | | PRED_UNIFY: (1), (42) imply: % 144.45/19.79 | | (43) $false % 144.45/19.79 | | % 144.45/19.79 | | CLOSE: (43) is inconsistent. % 144.45/19.79 | | % 144.45/19.79 | Case 2: % 144.45/19.79 | | % 144.45/19.79 | | (44) ~ isCountable0(slcrc0) % 144.45/19.79 | | % 144.45/19.79 | | GROUND_INST: instantiating (21) with all_91_0, all_116_0, xQ, simplifying % 144.45/19.79 | | with (31), (41) gives: % 144.45/19.79 | | (45) all_116_0 = all_91_0 % 144.45/19.79 | | % 144.45/19.79 | | GROUND_INST: instantiating (21) with xp, all_116_0, xQ, simplifying with % 144.45/19.79 | | (9), (41) gives: % 144.45/19.79 | | (46) all_116_0 = xp % 144.45/19.79 | | % 144.45/19.80 | | GROUND_INST: instantiating (22) with all_86_0, all_103_0, xm, xN, % 144.45/19.80 | | simplifying with (25), (35) gives: % 144.45/19.80 | | (47) all_103_0 = all_86_0 % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (22) with all_103_0, all_109_3, xm, xN, % 144.45/19.80 | | simplifying with (35), (37) gives: % 144.45/19.80 | | (48) all_109_3 = all_103_0 % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (22) with all_109_3, all_113_2, xm, xN, % 144.45/19.80 | | simplifying with (37), (39) gives: % 144.45/19.80 | | (49) all_113_2 = all_109_3 % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (22) with all_88_0, all_113_2, xm, xN, % 144.45/19.80 | | simplifying with (27), (39) gives: % 144.45/19.80 | | (50) all_113_2 = all_88_0 % 144.45/19.80 | | % 144.45/19.80 | | COMBINE_EQS: (45), (46) imply: % 144.45/19.80 | | (51) all_91_0 = xp % 144.45/19.80 | | % 144.45/19.80 | | SIMP: (51) implies: % 144.45/19.80 | | (52) all_91_0 = xp % 144.45/19.80 | | % 144.45/19.80 | | COMBINE_EQS: (49), (50) imply: % 144.45/19.80 | | (53) all_109_3 = all_88_0 % 144.45/19.80 | | % 144.45/19.80 | | SIMP: (53) implies: % 144.45/19.80 | | (54) all_109_3 = all_88_0 % 144.45/19.80 | | % 144.45/19.80 | | COMBINE_EQS: (48), (54) imply: % 144.45/19.80 | | (55) all_103_0 = all_88_0 % 144.45/19.80 | | % 144.45/19.80 | | SIMP: (55) implies: % 144.45/19.80 | | (56) all_103_0 = all_88_0 % 144.45/19.80 | | % 144.45/19.80 | | COMBINE_EQS: (47), (56) imply: % 144.45/19.80 | | (57) all_88_0 = all_86_0 % 144.45/19.80 | | % 144.45/19.80 | | REDUCE: (29), (52) imply: % 144.45/19.80 | | (58) ~ (xx = xp) % 144.45/19.80 | | % 144.45/19.80 | | SIMP: (58) implies: % 144.45/19.80 | | (59) ~ (xx = xp) % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (5) with xm, all_86_0, simplifying with (12), % 144.45/19.80 | | (19), (25) gives: % 144.45/19.80 | | (60) aSubsetOf0(all_86_0, szNzAzT0) % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (4) with xm, all_86_0, simplifying with (12), % 144.45/19.80 | | (19), (25) gives: % 144.45/19.80 | | (61) isCountable0(all_86_0) % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (6) with xm, xx, simplifying with (12), (13), % 144.45/19.80 | | (19) gives: % 144.45/19.80 | | (62) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & % 144.45/19.80 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) | % 144.45/19.80 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 144.45/19.80 | | % 144.45/19.80 | | DELTA: instantiating (62) with fresh symbol all_157_0 gives: % 144.45/19.80 | | (63) sdtlpdtrp0(xN, xm) = all_157_0 & szmzizndt0(all_157_0) = xx & % 144.45/19.80 | | $i(all_157_0) & $i(xx) & aElementOf0(xx, all_157_0) & ! [v0: $i] : % 144.45/19.80 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_157_0) | sdtlseqdt0(xx, v0)) % 144.45/19.80 | | % 144.45/19.80 | | ALPHA: (63) implies: % 144.45/19.80 | | (64) $i(all_157_0) % 144.45/19.80 | | (65) szmzizndt0(all_157_0) = xx % 144.45/19.80 | | (66) sdtlpdtrp0(xN, xm) = all_157_0 % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (22) with all_86_0, all_157_0, xm, xN, % 144.45/19.80 | | simplifying with (25), (66) gives: % 144.45/19.80 | | (67) all_157_0 = all_86_0 % 144.45/19.80 | | % 144.45/19.80 | | REDUCE: (65), (67) imply: % 144.45/19.80 | | (68) szmzizndt0(all_86_0) = xx % 144.45/19.80 | | % 144.45/19.80 | | REDUCE: (64), (67) imply: % 144.45/19.80 | | (69) $i(all_86_0) % 144.45/19.80 | | % 144.45/19.80 | | GROUND_INST: instantiating (3) with all_86_0, xQ, xx, xp, simplifying with % 144.45/19.80 | | (8), (9), (18), (24), (30), (60), (68), (69) gives: % 144.77/19.80 | | (70) all_86_0 = slcrc0 | xx = xp | xQ = slcrc0 % 144.77/19.80 | | % 144.77/19.80 | | BETA: splitting (70) gives: % 144.77/19.80 | | % 144.77/19.80 | | Case 1: % 144.77/19.80 | | | % 144.77/19.80 | | | (71) all_86_0 = slcrc0 % 144.77/19.80 | | | % 144.77/19.80 | | | REDUCE: (61), (71) imply: % 144.77/19.81 | | | (72) isCountable0(slcrc0) % 144.77/19.81 | | | % 144.77/19.81 | | | PRED_UNIFY: (44), (72) imply: % 144.77/19.81 | | | (73) $false % 144.77/19.81 | | | % 144.77/19.81 | | | CLOSE: (73) is inconsistent. % 144.77/19.81 | | | % 144.77/19.81 | | Case 2: % 144.77/19.81 | | | % 144.77/19.81 | | | (74) xx = xp | xQ = slcrc0 % 144.77/19.81 | | | % 144.77/19.81 | | | BETA: splitting (74) gives: % 144.77/19.81 | | | % 144.77/19.81 | | | Case 1: % 144.77/19.81 | | | | % 144.77/19.81 | | | | (75) xQ = slcrc0 % 144.77/19.81 | | | | % 144.77/19.81 | | | | REDUCE: (33), (75) imply: % 144.77/19.81 | | | | (76) $false % 144.77/19.81 | | | | % 144.77/19.81 | | | | CLOSE: (76) is inconsistent. % 144.77/19.81 | | | | % 144.77/19.81 | | | Case 2: % 144.77/19.81 | | | | % 144.77/19.81 | | | | (77) xx = xp % 144.77/19.81 | | | | % 144.77/19.81 | | | | REDUCE: (59), (77) imply: % 144.77/19.81 | | | | (78) $false % 144.77/19.81 | | | | % 144.77/19.81 | | | | CLOSE: (78) is inconsistent. % 144.77/19.81 | | | | % 144.77/19.81 | | | End of split % 144.77/19.81 | | | % 144.77/19.81 | | End of split % 144.77/19.81 | | % 144.77/19.81 | End of split % 144.77/19.81 | % 144.77/19.81 End of proof % 144.77/19.81 % SZS output end Proof for theBenchmark % 144.77/19.81 % 144.77/19.81 19178ms %------------------------------------------------------------------------------