%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM617+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 : n028.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 11:49:00 EDT 2023 % Result : Theorem 24.77s 4.06s % Output : Proof 48.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM617+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.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 12:20:06 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.34/1.59 Prover 4: Preprocessing ... % 6.34/1.59 Prover 1: Preprocessing ... % 6.64/1.60 Prover 2: Preprocessing ... % 6.64/1.61 Prover 3: Preprocessing ... % 6.64/1.61 Prover 0: Preprocessing ... % 6.94/1.65 Prover 5: Preprocessing ... % 6.94/1.66 Prover 6: Preprocessing ... % 18.42/3.21 Prover 3: Constructing countermodel ... % 18.42/3.22 Prover 1: Constructing countermodel ... % 18.98/3.25 Prover 6: Proving ... % 21.75/3.67 Prover 5: Proving ... % 24.77/4.06 Prover 3: proved (3422ms) % 24.77/4.06 % 24.77/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.77/4.06 % 24.77/4.06 Prover 6: stopped % 24.77/4.06 Prover 5: stopped % 24.77/4.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.77/4.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.77/4.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.11/4.28 Prover 8: Preprocessing ... % 27.71/4.44 Prover 10: Preprocessing ... % 27.71/4.44 Prover 7: Preprocessing ... % 29.93/4.69 Prover 8: Warning: ignoring some quantifiers % 30.08/4.71 Prover 8: Constructing countermodel ... % 34.80/5.37 Prover 7: Constructing countermodel ... % 34.80/5.38 Prover 10: Constructing countermodel ... % 40.16/6.04 Prover 10: Found proof (size 36) % 40.16/6.04 Prover 10: proved (1948ms) % 40.16/6.05 Prover 7: stopped % 40.16/6.05 Prover 8: stopped % 40.16/6.05 Prover 1: stopped % 44.83/6.80 Prover 2: Proving ... % 44.83/6.83 Prover 2: stopped % 45.79/6.96 Prover 4: Constructing countermodel ... % 45.79/6.99 Prover 4: stopped % 47.44/7.37 Prover 0: Proving ... % 47.44/7.42 Prover 0: stopped % 47.44/7.42 % 47.44/7.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 47.44/7.42 % 47.85/7.43 % SZS output start Proof for theBenchmark % 47.85/7.44 Assumptions after simplification: % 47.85/7.44 --------------------------------- % 47.85/7.44 % 47.85/7.44 (mDefSub) % 47.85/7.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.85/7.45 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 47.85/7.45 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 47.85/7.45 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 47.85/7.45 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 47.85/7.46 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 47.85/7.46 % 47.85/7.46 (mNATSet) % 47.85/7.46 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 47.85/7.46 % 47.85/7.46 (m__) % 47.85/7.46 $i(xx) & $i(szNzAzT0) & ~ aElementOf0(xx, szNzAzT0) % 47.85/7.46 % 47.85/7.46 (m__4730) % 48.09/7.51 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 48.09/7.51 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 48.09/7.51 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 48.09/7.51 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 48.09/7.51 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 48.09/7.51 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 48.09/7.51 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 48.09/7.51 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 48.09/7.51 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 48.09/7.51 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 48.09/7.51 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 48.09/7.51 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 48.09/7.51 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 48.09/7.51 % 48.09/7.51 (m__4758) % 48.09/7.52 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 48.09/7.52 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! % 48.09/7.52 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 48.09/7.52 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 48.09/7.52 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~ % 48.09/7.52 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & % 48.09/7.52 $i(v3) & aElementOf0(v3, v0)))) % 48.09/7.52 % 48.09/7.52 (m__4854) % 48.09/7.52 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = % 48.09/7.52 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 48.09/7.52 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = % 48.09/7.52 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & % 48.09/7.52 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 48.09/7.52 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ % 48.09/7.52 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 48.09/7.52 aElementOf0(v3, v1))) % 48.09/7.52 % 48.09/7.52 (m__4891) % 48.09/7.52 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 48.09/7.52 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 48.09/7.52 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 48.09/7.52 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 48.09/7.52 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 48.09/7.52 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 48.09/7.52 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 48.09/7.52 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 48.09/7.52 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 48.09/7.53 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 48.09/7.53 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 48.09/7.53 aElementOf0(v4, v1)))) % 48.09/7.53 % 48.09/7.53 (m__5106) % 48.09/7.53 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | % 48.09/7.53 ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0)) % 48.09/7.53 % 48.09/7.53 (m__5309) % 48.09/7.53 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 48.09/7.53 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, % 48.09/7.53 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) % 48.09/7.53 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 48.09/7.53 szNzAzT0)) % 48.09/7.53 % 48.09/7.53 (m__5348) % 48.09/7.53 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & % 48.09/7.53 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 48.09/7.53 % 48.09/7.53 (function-axioms) % 48.09/7.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.09/7.53 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 48.09/7.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 48.09/7.53 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 48.09/7.53 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 48.09/7.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 48.09/7.53 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 48.09/7.53 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 48.09/7.53 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 48.09/7.53 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 48.09/7.53 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 48.09/7.53 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 48.09/7.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 48.09/7.53 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 48.09/7.53 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 48.09/7.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 48.09/7.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.09/7.53 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 48.09/7.53 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 48.09/7.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.09/7.53 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 48.09/7.53 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 48.09/7.53 v0)) % 48.09/7.53 % 48.09/7.53 Further assumptions not needed in the proof: % 48.09/7.53 -------------------------------------------- % 48.09/7.54 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 48.09/7.54 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 48.09/7.54 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 48.09/7.54 mDefSeg, mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, % 48.09/7.54 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, % 48.09/7.54 mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, % 48.09/7.54 mLessTrans, mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, % 48.09/7.54 mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, % 48.09/7.54 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, % 48.09/7.54 mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, % 48.09/7.54 m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, % 48.09/7.54 m__4182, m__4331, m__4411, m__4618, m__4660, m__4908, m__4982, m__4998, m__5078, % 48.09/7.54 m__5093, m__5116, m__5147, m__5164, m__5173, m__5182, m__5195, m__5208, m__5217, % 48.09/7.54 m__5270, m__5321 % 48.09/7.54 % 48.09/7.54 Those formulas are unsatisfiable: % 48.09/7.54 --------------------------------- % 48.09/7.54 % 48.09/7.54 Begin of proof % 48.09/7.54 | % 48.09/7.54 | ALPHA: (mDefSub) implies: % 48.09/7.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 48.09/7.54 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 48.09/7.54 | aSet0(v0) | aElementOf0(v2, v0)) % 48.09/7.54 | % 48.09/7.54 | ALPHA: (mNATSet) implies: % 48.09/7.54 | (2) aSet0(szNzAzT0) % 48.09/7.54 | % 48.09/7.54 | ALPHA: (m__4730) implies: % 48.09/7.54 | (3) szDzozmdt0(xd) = szNzAzT0 % 48.09/7.54 | % 48.09/7.54 | ALPHA: (m__4758) implies: % 48.09/7.54 | (4) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 48.09/7.54 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] : % 48.09/7.54 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | % 48.09/7.54 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 48.09/7.54 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: % 48.09/7.54 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : % 48.09/7.54 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 48.09/7.54 | % 48.09/7.54 | ALPHA: (m__4854) implies: % 48.09/7.54 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 48.09/7.54 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 48.09/7.54 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] % 48.09/7.54 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 48.09/7.54 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 48.09/7.54 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 48.09/7.54 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) % 48.09/7.54 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1))) % 48.09/7.54 | % 48.09/7.54 | ALPHA: (m__4891) implies: % 48.09/7.55 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 48.09/7.55 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 48.09/7.55 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 48.09/7.55 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 48.09/7.55 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 48.09/7.55 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 48.09/7.55 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 48.09/7.55 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 48.09/7.55 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 48.09/7.55 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 48.09/7.55 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 48.09/7.55 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 48.09/7.55 | $i(v4) & aElementOf0(v4, v1)))) % 48.09/7.55 | % 48.09/7.55 | ALPHA: (m__5106) implies: % 48.09/7.55 | (7) aSubsetOf0(xQ, szNzAzT0) % 48.09/7.55 | % 48.09/7.55 | ALPHA: (m__5309) implies: % 48.09/7.55 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 & % 48.09/7.55 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe, % 48.09/7.55 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) & % 48.09/7.55 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 48.09/7.55 | szNzAzT0)) % 48.09/7.55 | % 48.09/7.55 | ALPHA: (m__5348) implies: % 48.09/7.55 | (9) $i(xQ) % 48.09/7.55 | (10) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) & % 48.09/7.55 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 48.09/7.55 | % 48.09/7.55 | ALPHA: (m__) implies: % 48.09/7.55 | (11) ~ aElementOf0(xx, szNzAzT0) % 48.09/7.55 | (12) $i(xx) % 48.09/7.55 | % 48.09/7.55 | ALPHA: (function-axioms) implies: % 48.09/7.55 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.09/7.55 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 48.09/7.55 | % 48.43/7.55 | DELTA: instantiating (10) with fresh symbol all_86_0 gives: % 48.43/7.55 | (14) ~ (all_86_0 = xx) & szmzizndt0(xQ) = all_86_0 & $i(all_86_0) & % 48.43/7.55 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx) % 48.43/7.55 | % 48.43/7.55 | ALPHA: (14) implies: % 48.43/7.55 | (15) aElementOf0(xx, xQ) % 48.43/7.55 | % 48.43/7.55 | DELTA: instantiating (8) with fresh symbols all_99_0, all_99_1, all_99_2 % 48.43/7.55 | gives: % 48.43/7.55 | (16) szDzizrdt0(xd) = all_99_1 & sdtlbdtrb0(xd, all_99_1) = all_99_0 & % 48.43/7.55 | sdtlpdtrp0(xd, xn) = all_99_1 & sdtlpdtrp0(xe, xn) = xp & % 48.43/7.55 | szDzozmdt0(xd) = all_99_2 & $i(all_99_0) & $i(all_99_1) & $i(all_99_2) % 48.43/7.55 | & aElementOf0(xn, all_99_0) & aElementOf0(xn, all_99_2) & % 48.43/7.55 | aElementOf0(xn, szNzAzT0) % 48.43/7.55 | % 48.43/7.55 | ALPHA: (16) implies: % 48.43/7.55 | (17) $i(all_99_2) % 48.43/7.55 | (18) szDzozmdt0(xd) = all_99_2 % 48.43/7.55 | % 48.43/7.55 | DELTA: instantiating (4) with fresh symbols all_104_0, all_104_1 gives: % 48.43/7.56 | (19) sdtlcdtrc0(xd, all_104_1) = all_104_0 & szDzozmdt0(xd) = all_104_1 & % 48.43/7.56 | $i(all_104_0) & $i(all_104_1) & aSubsetOf0(all_104_0, xT) & % 48.43/7.56 | aSet0(all_104_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) % 48.43/7.56 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_104_1) | % 48.43/7.56 | aElementOf0(v0, all_104_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 48.43/7.56 | aElementOf0(v0, all_104_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( % 48.43/7.56 | ~ $i(v0) | ~ aElementOf0(v0, all_104_0) | ? [v1: $i] : % 48.43/7.56 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_104_1))) % 48.43/7.56 | % 48.43/7.56 | ALPHA: (19) implies: % 48.43/7.56 | (20) szDzozmdt0(xd) = all_104_1 % 48.43/7.56 | % 48.43/7.56 | DELTA: instantiating (5) with fresh symbols all_107_0, all_107_1, all_107_2 % 48.43/7.56 | gives: % 48.43/7.56 | (21) szDzizrdt0(xd) = all_107_2 & sdtlbdtrb0(xd, all_107_2) = all_107_1 & % 48.43/7.56 | szDzozmdt0(xd) = all_107_0 & $i(all_107_0) & $i(all_107_1) & % 48.43/7.56 | $i(all_107_2) & aElementOf0(all_107_2, xT) & aSet0(all_107_1) & ! % 48.43/7.56 | [v0: $i] : ! [v1: int] : (v1 = all_107_2 | ~ (sdtlpdtrp0(xd, v0) = % 48.43/7.56 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_107_1)) & ! [v0: $i] : % 48.43/7.56 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 48.43/7.56 | aElementOf0(v0, all_107_1) | aElementOf0(v0, all_107_0)) & ! [v0: % 48.43/7.56 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_107_2) | ~ $i(v0) | ~ % 48.43/7.56 | aElementOf0(v0, all_107_0) | aElementOf0(v0, all_107_1)) % 48.43/7.56 | % 48.43/7.56 | ALPHA: (21) implies: % 48.43/7.56 | (22) szDzozmdt0(xd) = all_107_0 % 48.43/7.56 | % 48.43/7.56 | DELTA: instantiating (6) with fresh symbols all_113_0, all_113_1, all_113_2 % 48.43/7.56 | gives: % 48.43/7.56 | (23) szDzizrdt0(xd) = all_113_2 & sdtlcdtrc0(xe, all_113_1) = xO & % 48.43/7.56 | sdtlbdtrb0(xd, all_113_2) = all_113_1 & szDzozmdt0(xd) = all_113_0 & % 48.43/7.56 | $i(all_113_0) & $i(all_113_1) & $i(all_113_2) & aSet0(all_113_1) & % 48.43/7.56 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_113_2 | ~ % 48.43/7.56 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 48.43/7.56 | all_113_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 48.43/7.56 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_113_1) | % 48.43/7.56 | aElementOf0(v0, all_113_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 48.43/7.56 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 48.43/7.56 | aElementOf0(v1, all_113_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 48.43/7.56 | ~ (sdtlpdtrp0(xd, v0) = all_113_2) | ~ $i(v0) | ~ aElementOf0(v0, % 48.43/7.56 | all_113_0) | aElementOf0(v0, all_113_1)) & ! [v0: $i] : ( ~ % 48.43/7.56 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 48.43/7.56 | = v0 & $i(v1) & aElementOf0(v1, all_113_1))) % 48.43/7.56 | % 48.43/7.56 | ALPHA: (23) implies: % 48.43/7.56 | (24) szDzozmdt0(xd) = all_113_0 % 48.43/7.56 | % 48.43/7.56 | GROUND_INST: instantiating (13) with szNzAzT0, all_107_0, xd, simplifying with % 48.43/7.56 | (3), (22) gives: % 48.43/7.56 | (25) all_107_0 = szNzAzT0 % 48.43/7.56 | % 48.43/7.56 | GROUND_INST: instantiating (13) with all_107_0, all_113_0, xd, simplifying % 48.43/7.56 | with (22), (24) gives: % 48.43/7.56 | (26) all_113_0 = all_107_0 % 48.43/7.56 | % 48.43/7.56 | GROUND_INST: instantiating (13) with all_104_1, all_113_0, xd, simplifying % 48.43/7.56 | with (20), (24) gives: % 48.43/7.56 | (27) all_113_0 = all_104_1 % 48.43/7.56 | % 48.43/7.56 | GROUND_INST: instantiating (13) with all_99_2, all_113_0, xd, simplifying with % 48.43/7.56 | (18), (24) gives: % 48.43/7.56 | (28) all_113_0 = all_99_2 % 48.43/7.56 | % 48.43/7.56 | COMBINE_EQS: (26), (27) imply: % 48.43/7.56 | (29) all_107_0 = all_104_1 % 48.43/7.56 | % 48.43/7.56 | SIMP: (29) implies: % 48.43/7.56 | (30) all_107_0 = all_104_1 % 48.43/7.56 | % 48.43/7.56 | COMBINE_EQS: (27), (28) imply: % 48.43/7.56 | (31) all_104_1 = all_99_2 % 48.43/7.56 | % 48.43/7.57 | COMBINE_EQS: (25), (30) imply: % 48.43/7.57 | (32) all_104_1 = szNzAzT0 % 48.43/7.57 | % 48.43/7.57 | SIMP: (32) implies: % 48.43/7.57 | (33) all_104_1 = szNzAzT0 % 48.43/7.57 | % 48.43/7.57 | COMBINE_EQS: (31), (33) imply: % 48.43/7.57 | (34) all_99_2 = szNzAzT0 % 48.43/7.57 | % 48.43/7.57 | SIMP: (34) implies: % 48.43/7.57 | (35) all_99_2 = szNzAzT0 % 48.43/7.57 | % 48.43/7.57 | REDUCE: (17), (35) imply: % 48.43/7.57 | (36) $i(szNzAzT0) % 48.43/7.57 | % 48.43/7.57 | GROUND_INST: instantiating (1) with szNzAzT0, xQ, xx, simplifying with (2), % 48.51/7.57 | (7), (9), (11), (12), (15), (36) gives: % 48.51/7.57 | (37) $false % 48.51/7.57 | % 48.51/7.57 | CLOSE: (37) is inconsistent. % 48.51/7.57 | % 48.51/7.57 End of proof % 48.51/7.57 % SZS output end Proof for theBenchmark % 48.51/7.57 % 48.51/7.57 6969ms %------------------------------------------------------------------------------