%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM598+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 11:48:51 EDT 2023 % Result : Theorem 134.47s 18.88s % Output : Proof 134.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM598+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 12:36:34 EDT 2023 % 0.14/0.36 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.02/1.62 Prover 1: Preprocessing ... % 6.02/1.62 Prover 4: Preprocessing ... % 6.15/1.64 Prover 3: Preprocessing ... % 6.15/1.64 Prover 0: Preprocessing ... % 6.15/1.64 Prover 5: Preprocessing ... % 6.15/1.64 Prover 2: Preprocessing ... % 6.15/1.67 Prover 6: Preprocessing ... % 14.63/2.90 Prover 1: Constructing countermodel ... % 14.63/2.90 Prover 3: Constructing countermodel ... % 14.63/2.94 Prover 6: Proving ... % 16.71/3.10 Prover 5: Proving ... % 18.48/3.35 Prover 2: Proving ... % 22.27/3.89 Prover 4: Constructing countermodel ... % 24.99/4.28 Prover 0: Proving ... % 70.62/10.35 Prover 2: stopped % 70.62/10.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.79/10.50 Prover 7: Preprocessing ... % 73.97/10.78 Prover 7: Constructing countermodel ... % 97.93/14.01 Prover 5: stopped % 97.93/14.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 98.38/14.17 Prover 8: Preprocessing ... % 100.59/14.36 Prover 8: Warning: ignoring some quantifiers % 100.59/14.39 Prover 8: Constructing countermodel ... % 113.00/16.00 Prover 1: stopped % 113.00/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 114.07/16.15 Prover 9: Preprocessing ... % 118.71/16.83 Prover 9: Constructing countermodel ... % 127.12/17.92 Prover 6: stopped % 127.12/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 127.55/18.05 Prover 10: Preprocessing ... % 129.47/18.26 Prover 10: Constructing countermodel ... % 134.37/18.87 Prover 10: Found proof (size 60) % 134.37/18.87 Prover 10: proved (946ms) % 134.37/18.87 Prover 9: stopped % 134.47/18.87 Prover 0: stopped % 134.47/18.87 Prover 7: stopped % 134.47/18.87 Prover 8: stopped % 134.47/18.88 Prover 3: stopped % 134.47/18.88 Prover 4: stopped % 134.47/18.88 % 134.47/18.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 134.47/18.88 % 134.47/18.89 % SZS output start Proof for theBenchmark % 134.47/18.89 Assumptions after simplification: % 134.47/18.89 --------------------------------- % 134.47/18.89 % 134.47/18.89 (mDefPtt) % 134.56/18.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 134.56/18.93 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] : % 134.56/18.93 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 134.56/18.93 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, % 134.56/18.93 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~ % 134.56/18.93 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & ! % 134.56/18.93 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i] % 134.56/18.93 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 = % 134.56/18.93 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4) % 134.56/18.93 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & ! % 134.56/18.93 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~ % 134.56/18.93 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2)))) % 134.56/18.93 % 134.56/18.93 (mEOfElem) % 134.56/18.93 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 134.56/18.93 ~ aSet0(v0) | aElement0(v1)) % 134.56/18.93 % 134.56/18.93 (mImgCount) % 134.56/18.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0, % 134.56/18.93 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 134.56/18.93 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ isCountable0(v2) | % 134.56/18.93 isCountable0(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & % 134.56/18.93 sdtlpdtrp0(v0, v5) = v6 & sdtlpdtrp0(v0, v4) = v6 & $i(v6) & $i(v5) & % 134.56/18.93 $i(v4) & aElementOf0(v5, v1) & aElementOf0(v4, v1))) % 134.56/18.93 % 134.56/18.93 (mPttSet) % 134.56/18.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 134.68/18.94 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] : % 134.68/18.94 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3))) % 134.68/18.94 % 134.68/18.94 (m__) % 134.68/18.94 $i(xO) & ~ isCountable0(xO) % 134.68/18.94 % 134.68/18.94 (m__3291) % 134.68/18.94 $i(xT) & isFinite0(xT) & aSet0(xT) % 134.68/18.94 % 134.68/18.94 (m__3821) % 134.68/18.94 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 134.68/18.94 : (v1 = v0 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ % 134.68/18.94 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, % 134.68/18.94 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & szmzizndt0(v3) = % 134.68/18.94 v5 & szmzizndt0(v2) = v4 & $i(v5) & $i(v4))) % 134.68/18.94 % 134.68/18.94 (m__4660) % 134.68/18.94 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 134.68/18.94 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 134.68/18.94 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 134.68/18.94 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 134.68/18.94 % 134.68/18.94 (m__4730) % 134.68/18.95 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 134.68/18.95 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | % 134.68/18.95 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 134.68/18.95 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 134.68/18.95 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 134.68/18.95 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ % 134.68/18.95 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 134.68/18.95 aSet0(v6)))) % 134.68/18.95 % 134.68/18.95 (m__4758) % 134.68/18.95 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 134.68/18.95 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 134.68/18.95 % 134.68/18.95 (m__4854) % 134.68/18.95 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 134.68/18.95 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) & % 134.68/18.95 aElementOf0(v0, xT)) % 134.68/18.95 % 134.68/18.95 (m__4891) % 134.68/18.95 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 134.68/18.95 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 134.68/18.95 aSet0(xO)) % 134.68/18.95 % 134.68/18.95 (function-axioms) % 134.68/18.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 134.68/18.96 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 134.68/18.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 134.68/18.96 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 134.68/18.96 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 134.68/18.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 134.68/18.96 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 134.68/18.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 134.68/18.96 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 134.68/18.96 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 134.68/18.96 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 134.68/18.96 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 134.68/18.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 134.68/18.96 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 134.68/18.96 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 134.68/18.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 134.68/18.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 134.68/18.96 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 134.68/18.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 134.68/18.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 134.68/18.96 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 134.68/18.96 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 134.68/18.96 v0)) % 134.68/18.96 % 134.68/18.96 Further assumptions not needed in the proof: % 134.68/18.96 -------------------------------------------- % 134.68/18.96 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 134.68/18.96 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 134.68/18.96 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg, % 134.68/18.96 mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet, % 134.68/18.96 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mImgRng, % 134.68/18.96 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, % 134.68/18.96 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, % 134.68/18.96 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 134.68/18.96 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 134.68/18.96 mZeroNum, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, % 134.68/18.96 m__3623, m__3671, m__3754, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618 % 134.68/18.96 % 134.68/18.96 Those formulas are unsatisfiable: % 134.68/18.96 --------------------------------- % 134.68/18.96 % 134.68/18.96 Begin of proof % 134.68/18.96 | % 134.68/18.97 | ALPHA: (m__3291) implies: % 134.68/18.97 | (1) aSet0(xT) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__3821) implies: % 134.68/18.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 134.68/18.97 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) % 134.68/18.97 | | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, % 134.68/18.97 | szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & % 134.68/18.97 | szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v5) & $i(v4))) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__4660) implies: % 134.68/18.97 | (3) aFunction0(xe) % 134.68/18.97 | (4) szDzozmdt0(xe) = szNzAzT0 % 134.68/18.97 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 134.68/18.97 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 134.68/18.97 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__4730) implies: % 134.68/18.97 | (6) aFunction0(xd) % 134.68/18.97 | (7) szDzozmdt0(xd) = szNzAzT0 % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__4758) implies: % 134.68/18.97 | (8) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 134.68/18.97 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__4854) implies: % 134.68/18.97 | (9) $i(xT) % 134.68/18.97 | (10) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 134.68/18.97 | = v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT)) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__4891) implies: % 134.68/18.97 | (11) $i(xe) % 134.68/18.97 | (12) $i(xd) % 134.68/18.97 | (13) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) % 134.68/18.97 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (m__) implies: % 134.68/18.97 | (14) ~ isCountable0(xO) % 134.68/18.97 | % 134.68/18.97 | ALPHA: (function-axioms) implies: % 134.68/18.97 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 134.68/18.97 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 134.68/18.97 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 134.68/18.97 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 134.68/18.98 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 134.68/18.98 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0)) % 134.68/18.98 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 134.68/18.98 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 134.68/18.98 | % 134.68/18.98 | DELTA: instantiating (8) with fresh symbols all_76_0, all_76_1 gives: % 134.68/18.98 | (19) sdtlcdtrc0(xd, all_76_1) = all_76_0 & szDzozmdt0(xd) = all_76_1 & % 134.68/18.98 | $i(all_76_0) & $i(all_76_1) & aSubsetOf0(all_76_0, xT) % 134.68/18.98 | % 134.68/18.98 | ALPHA: (19) implies: % 134.68/18.98 | (20) szDzozmdt0(xd) = all_76_1 % 134.68/18.98 | % 134.68/18.98 | DELTA: instantiating (13) with fresh symbols all_78_0, all_78_1 gives: % 134.68/18.98 | (21) szDzizrdt0(xd) = all_78_1 & sdtlcdtrc0(xe, all_78_0) = xO & % 134.68/18.98 | sdtlbdtrb0(xd, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1) & % 134.68/18.98 | aSet0(xO) % 134.68/18.98 | % 134.68/18.98 | ALPHA: (21) implies: % 134.68/18.98 | (22) sdtlbdtrb0(xd, all_78_1) = all_78_0 % 134.68/18.98 | (23) sdtlcdtrc0(xe, all_78_0) = xO % 134.68/18.98 | (24) szDzizrdt0(xd) = all_78_1 % 134.68/18.98 | % 134.68/18.98 | DELTA: instantiating (10) with fresh symbols all_80_0, all_80_1 gives: % 134.68/18.98 | (25) szDzizrdt0(xd) = all_80_1 & sdtlbdtrb0(xd, all_80_1) = all_80_0 & % 134.68/18.98 | $i(all_80_0) & $i(all_80_1) & isCountable0(all_80_0) & % 134.68/18.98 | aElementOf0(all_80_1, xT) % 134.68/18.98 | % 134.68/18.98 | ALPHA: (25) implies: % 134.68/18.98 | (26) aElementOf0(all_80_1, xT) % 134.68/18.98 | (27) isCountable0(all_80_0) % 134.68/18.98 | (28) $i(all_80_1) % 134.68/18.98 | (29) $i(all_80_0) % 134.68/18.98 | (30) sdtlbdtrb0(xd, all_80_1) = all_80_0 % 134.68/18.98 | (31) szDzizrdt0(xd) = all_80_1 % 134.68/18.98 | % 134.68/18.98 | GROUND_INST: instantiating (16) with szNzAzT0, all_76_1, xd, simplifying with % 134.68/18.98 | (7), (20) gives: % 134.68/18.98 | (32) all_76_1 = szNzAzT0 % 134.68/18.98 | % 134.68/18.98 | GROUND_INST: instantiating (17) with all_78_1, all_80_1, xd, simplifying with % 134.68/18.98 | (24), (31) gives: % 134.68/18.98 | (33) all_80_1 = all_78_1 % 134.68/18.98 | % 134.68/18.98 | REDUCE: (30), (33) imply: % 134.68/18.98 | (34) sdtlbdtrb0(xd, all_78_1) = all_80_0 % 134.68/18.98 | % 134.68/18.98 | REDUCE: (28), (33) imply: % 134.68/18.98 | (35) $i(all_78_1) % 134.68/18.98 | % 134.68/18.98 | REDUCE: (26), (33) imply: % 134.68/18.98 | (36) aElementOf0(all_78_1, xT) % 134.68/18.98 | % 134.68/18.98 | GROUND_INST: instantiating (18) with all_78_0, all_80_0, all_78_1, xd, % 134.68/18.98 | simplifying with (22), (34) gives: % 134.68/18.98 | (37) all_80_0 = all_78_0 % 134.68/18.98 | % 134.68/18.98 | REDUCE: (29), (37) imply: % 134.68/18.98 | (38) $i(all_78_0) % 134.68/18.98 | % 134.68/18.98 | REDUCE: (27), (37) imply: % 134.68/18.98 | (39) isCountable0(all_78_0) % 134.68/18.98 | % 134.68/18.98 | GROUND_INST: instantiating (mEOfElem) with xT, all_78_1, simplifying with (1), % 134.68/18.98 | (9), (35), (36) gives: % 134.68/18.98 | (40) aElement0(all_78_1) % 134.68/18.98 | % 134.68/18.98 | GROUND_INST: instantiating (mPttSet) with xd, all_78_1, all_78_0, simplifying % 134.68/18.98 | with (6), (12), (22), (35), (40) gives: % 134.68/18.98 | (41) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_78_0, % 134.68/18.98 | v0)) % 134.68/18.98 | % 134.68/18.99 | GROUND_INST: instantiating (mDefPtt) with xd, all_78_1, all_78_0, simplifying % 134.68/18.99 | with (6), (12), (22), (35), (40) gives: % 134.68/18.99 | (42) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 134.68/18.99 | int] : (v2 = all_78_1 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | % 134.68/18.99 | ~ $i(all_78_0) | ~ aElementOf0(v1, all_78_0)) & ! [v1: $i] : ! % 134.68/18.99 | [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ % 134.68/18.99 | $i(all_78_0) | ~ aElementOf0(v1, all_78_0) | aElementOf0(v1, v0)) % 134.68/18.99 | & ! [v1: any] : (v1 = all_78_0 | ~ $i(v1) | ~ aSet0(v1) | ? [v2: % 134.68/18.99 | $i] : ? [v3: any] : ($i(v2) & ( ~ aElementOf0(v2, v1) | ~ % 134.68/18.99 | aElementOf0(v2, v0) | ( ~ (v3 = all_78_1) & sdtlpdtrp0(xd, v2) % 134.68/18.99 | = v3 & $i(v3))) & (aElementOf0(v2, v1) | (v3 = all_78_1 & % 134.68/18.99 | sdtlpdtrp0(xd, v2) = all_78_1 & aElementOf0(v2, v0))))) & ! % 134.68/18.99 | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) = all_78_1) | ~ $i(v1) | ~ % 134.68/18.99 | $i(all_78_0) | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_78_0)) % 134.68/18.99 | & ( ~ $i(all_78_0) | aSet0(all_78_0))) % 134.68/18.99 | % 134.68/18.99 | DELTA: instantiating (41) with fresh symbol all_123_0 gives: % 134.68/18.99 | (43) szDzozmdt0(xd) = all_123_0 & $i(all_123_0) & aSubsetOf0(all_78_0, % 134.68/18.99 | all_123_0) % 134.68/18.99 | % 134.68/18.99 | ALPHA: (43) implies: % 134.68/18.99 | (44) aSubsetOf0(all_78_0, all_123_0) % 134.68/18.99 | (45) szDzozmdt0(xd) = all_123_0 % 134.68/18.99 | % 134.68/18.99 | DELTA: instantiating (42) with fresh symbol all_129_0 gives: % 134.68/18.99 | (46) szDzozmdt0(xd) = all_129_0 & $i(all_129_0) & ! [v0: $i] : ! [v1: % 134.68/18.99 | int] : (v1 = all_78_1 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | % 134.68/18.99 | ~ $i(all_78_0) | ~ aElementOf0(v0, all_78_0)) & ! [v0: $i] : ! % 134.68/18.99 | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ $i(all_78_0) % 134.68/18.99 | | ~ aElementOf0(v0, all_78_0) | aElementOf0(v0, all_129_0)) & ! % 134.68/18.99 | [v0: any] : (v0 = all_78_0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] : % 134.68/18.99 | ? [v2: any] : ($i(v1) & ( ~ aElementOf0(v1, v0) | ~ aElementOf0(v1, % 134.68/18.99 | all_129_0) | ( ~ (v2 = all_78_1) & sdtlpdtrp0(xd, v1) = v2 & % 134.68/18.99 | $i(v2))) & (aElementOf0(v1, v0) | (v2 = all_78_1 & % 134.68/18.99 | sdtlpdtrp0(xd, v1) = all_78_1 & aElementOf0(v1, all_129_0))))) % 134.68/18.99 | & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_78_1) | ~ $i(v0) | ~ % 134.68/18.99 | $i(all_78_0) | ~ aElementOf0(v0, all_129_0) | aElementOf0(v0, % 134.68/18.99 | all_78_0)) & ( ~ $i(all_78_0) | aSet0(all_78_0)) % 134.68/18.99 | % 134.68/18.99 | ALPHA: (46) implies: % 134.68/18.99 | (47) szDzozmdt0(xd) = all_129_0 % 134.68/18.99 | (48) ~ $i(all_78_0) | aSet0(all_78_0) % 134.68/18.99 | % 134.68/18.99 | BETA: splitting (48) gives: % 134.68/18.99 | % 134.68/18.99 | Case 1: % 134.68/18.99 | | % 134.68/18.99 | | (49) ~ $i(all_78_0) % 134.68/18.99 | | % 134.68/18.99 | | PRED_UNIFY: (38), (49) imply: % 134.68/19.00 | | (50) $false % 134.68/19.00 | | % 134.68/19.00 | | CLOSE: (50) is inconsistent. % 134.68/19.00 | | % 134.68/19.00 | Case 2: % 134.68/19.00 | | % 134.68/19.00 | | % 134.68/19.00 | | GROUND_INST: instantiating (16) with szNzAzT0, all_129_0, xd, simplifying % 134.68/19.00 | | with (7), (47) gives: % 134.68/19.00 | | (51) all_129_0 = szNzAzT0 % 134.68/19.00 | | % 134.68/19.00 | | GROUND_INST: instantiating (16) with all_123_0, all_129_0, xd, simplifying % 134.68/19.00 | | with (45), (47) gives: % 134.68/19.00 | | (52) all_129_0 = all_123_0 % 134.68/19.00 | | % 134.68/19.00 | | COMBINE_EQS: (51), (52) imply: % 134.68/19.00 | | (53) all_123_0 = szNzAzT0 % 134.68/19.00 | | % 134.68/19.00 | | REDUCE: (44), (53) imply: % 134.68/19.00 | | (54) aSubsetOf0(all_78_0, szNzAzT0) % 134.68/19.00 | | % 134.68/19.00 | | GROUND_INST: instantiating (mImgCount) with xe, szNzAzT0, all_78_0, xO, % 134.68/19.00 | | simplifying with (3), (4), (11), (14), (23), (38), (39), (54) % 134.68/19.00 | | gives: % 134.68/19.00 | | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 134.68/19.00 | | sdtlpdtrp0(xe, v1) = v2 & sdtlpdtrp0(xe, v0) = v2 & $i(v2) & % 134.68/19.00 | | $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0) & aElementOf0(v0, % 134.68/19.00 | | szNzAzT0)) % 134.68/19.00 | | % 134.68/19.00 | | DELTA: instantiating (55) with fresh symbols all_152_0, all_152_1, all_152_2 % 134.68/19.00 | | gives: % 134.68/19.00 | | (56) ~ (all_152_1 = all_152_2) & sdtlpdtrp0(xe, all_152_1) = all_152_0 & % 134.68/19.00 | | sdtlpdtrp0(xe, all_152_2) = all_152_0 & $i(all_152_0) & % 134.68/19.00 | | $i(all_152_1) & $i(all_152_2) & aElementOf0(all_152_1, szNzAzT0) & % 134.68/19.00 | | aElementOf0(all_152_2, szNzAzT0) % 134.68/19.00 | | % 134.68/19.00 | | ALPHA: (56) implies: % 134.68/19.00 | | (57) ~ (all_152_1 = all_152_2) % 134.68/19.00 | | (58) aElementOf0(all_152_2, szNzAzT0) % 134.68/19.00 | | (59) aElementOf0(all_152_1, szNzAzT0) % 134.68/19.00 | | (60) $i(all_152_2) % 134.68/19.00 | | (61) $i(all_152_1) % 134.68/19.00 | | (62) sdtlpdtrp0(xe, all_152_2) = all_152_0 % 134.68/19.00 | | (63) sdtlpdtrp0(xe, all_152_1) = all_152_0 % 134.68/19.00 | | % 134.68/19.00 | | GROUND_INST: instantiating (5) with all_152_2, all_152_0, simplifying with % 134.68/19.00 | | (58), (60), (62) gives: % 134.68/19.00 | | (64) ? [v0: $i] : (sdtlpdtrp0(xN, all_152_2) = v0 & szmzizndt0(v0) = % 134.68/19.00 | | all_152_0 & $i(v0) & $i(all_152_0)) % 134.68/19.00 | | % 134.68/19.00 | | GROUND_INST: instantiating (5) with all_152_1, all_152_0, simplifying with % 134.68/19.00 | | (59), (61), (63) gives: % 134.68/19.00 | | (65) ? [v0: $i] : (sdtlpdtrp0(xN, all_152_1) = v0 & szmzizndt0(v0) = % 134.68/19.00 | | all_152_0 & $i(v0) & $i(all_152_0)) % 134.68/19.00 | | % 134.68/19.00 | | DELTA: instantiating (65) with fresh symbol all_182_0 gives: % 134.68/19.00 | | (66) sdtlpdtrp0(xN, all_152_1) = all_182_0 & szmzizndt0(all_182_0) = % 134.68/19.00 | | all_152_0 & $i(all_182_0) & $i(all_152_0) % 134.68/19.00 | | % 134.68/19.00 | | ALPHA: (66) implies: % 134.68/19.00 | | (67) szmzizndt0(all_182_0) = all_152_0 % 134.68/19.00 | | (68) sdtlpdtrp0(xN, all_152_1) = all_182_0 % 134.68/19.00 | | % 134.68/19.00 | | DELTA: instantiating (64) with fresh symbol all_184_0 gives: % 134.68/19.00 | | (69) sdtlpdtrp0(xN, all_152_2) = all_184_0 & szmzizndt0(all_184_0) = % 134.68/19.00 | | all_152_0 & $i(all_184_0) & $i(all_152_0) % 134.68/19.00 | | % 134.68/19.00 | | ALPHA: (69) implies: % 134.68/19.00 | | (70) szmzizndt0(all_184_0) = all_152_0 % 134.68/19.01 | | (71) sdtlpdtrp0(xN, all_152_2) = all_184_0 % 134.68/19.01 | | % 134.68/19.01 | | GROUND_INST: instantiating (2) with all_152_1, all_152_2, all_182_0, % 134.68/19.01 | | all_184_0, simplifying with (58), (59), (60), (61), (68), (71) % 134.68/19.01 | | gives: % 134.68/19.01 | | (72) all_152_1 = all_152_2 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 134.68/19.01 | | szmzizndt0(all_184_0) = v1 & szmzizndt0(all_182_0) = v0 & $i(v1) & % 134.68/19.01 | | $i(v0)) % 134.68/19.01 | | % 134.68/19.01 | | BETA: splitting (72) gives: % 134.68/19.01 | | % 134.68/19.01 | | Case 1: % 134.68/19.01 | | | % 134.68/19.01 | | | (73) all_152_1 = all_152_2 % 134.68/19.01 | | | % 134.68/19.01 | | | REDUCE: (57), (73) imply: % 134.68/19.01 | | | (74) $false % 134.68/19.01 | | | % 134.68/19.01 | | | CLOSE: (74) is inconsistent. % 134.68/19.01 | | | % 134.68/19.01 | | Case 2: % 134.68/19.01 | | | % 134.68/19.01 | | | (75) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & szmzizndt0(all_184_0) % 134.68/19.01 | | | = v1 & szmzizndt0(all_182_0) = v0 & $i(v1) & $i(v0)) % 134.68/19.01 | | | % 134.68/19.01 | | | DELTA: instantiating (75) with fresh symbols all_228_0, all_228_1 gives: % 134.68/19.01 | | | (76) ~ (all_228_0 = all_228_1) & szmzizndt0(all_184_0) = all_228_0 & % 134.68/19.01 | | | szmzizndt0(all_182_0) = all_228_1 & $i(all_228_0) & $i(all_228_1) % 134.68/19.01 | | | % 134.68/19.01 | | | ALPHA: (76) implies: % 134.68/19.01 | | | (77) ~ (all_228_0 = all_228_1) % 134.68/19.01 | | | (78) szmzizndt0(all_182_0) = all_228_1 % 134.68/19.01 | | | (79) szmzizndt0(all_184_0) = all_228_0 % 134.68/19.01 | | | % 134.68/19.01 | | | GROUND_INST: instantiating (15) with all_152_0, all_228_1, all_182_0, % 134.68/19.01 | | | simplifying with (67), (78) gives: % 134.68/19.01 | | | (80) all_228_1 = all_152_0 % 134.68/19.01 | | | % 134.68/19.01 | | | GROUND_INST: instantiating (15) with all_152_0, all_228_0, all_184_0, % 134.68/19.01 | | | simplifying with (70), (79) gives: % 134.68/19.01 | | | (81) all_228_0 = all_152_0 % 134.68/19.01 | | | % 134.68/19.01 | | | REDUCE: (77), (80), (81) imply: % 134.68/19.01 | | | (82) $false % 134.68/19.01 | | | % 134.68/19.01 | | | CLOSE: (82) is inconsistent. % 134.68/19.01 | | | % 134.68/19.01 | | End of split % 134.68/19.01 | | % 134.68/19.01 | End of split % 134.68/19.01 | % 134.68/19.01 End of proof % 134.68/19.01 % SZS output end Proof for theBenchmark % 134.68/19.01 % 134.68/19.01 18368ms %------------------------------------------------------------------------------