%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM594+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 : n020.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 11:48:50 EDT 2023 % Result : Theorem 89.12s 12.53s % Output : Proof 89.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM594+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 15:42:30 EDT 2023 % 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.27/1.35 Prover 1: Preprocessing ... % 4.27/1.38 Prover 4: Preprocessing ... % 4.27/1.40 Prover 3: Preprocessing ... % 4.27/1.40 Prover 6: Preprocessing ... % 4.27/1.40 Prover 5: Preprocessing ... % 4.27/1.40 Prover 0: Preprocessing ... % 4.27/1.40 Prover 2: Preprocessing ... % 14.58/2.66 Prover 1: Constructing countermodel ... % 14.58/2.69 Prover 3: Constructing countermodel ... % 14.58/2.69 Prover 6: Proving ... % 14.58/2.77 Prover 5: Proving ... % 16.72/2.98 Prover 2: Proving ... % 20.30/3.44 Prover 4: Constructing countermodel ... % 20.30/3.50 Prover 0: Proving ... % 72.80/10.34 Prover 2: stopped % 72.80/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.62/10.46 Prover 7: Preprocessing ... % 75.07/10.64 Prover 7: Constructing countermodel ... % 89.12/12.51 Prover 7: Found proof (size 39) % 89.12/12.51 Prover 7: proved (2173ms) % 89.12/12.51 Prover 5: stopped % 89.12/12.51 Prover 6: stopped % 89.12/12.52 Prover 0: stopped % 89.12/12.52 Prover 1: stopped % 89.12/12.52 Prover 4: stopped % 89.12/12.53 Prover 3: stopped % 89.12/12.53 % 89.12/12.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 89.12/12.53 % 89.12/12.53 % SZS output start Proof for theBenchmark % 89.12/12.54 Assumptions after simplification: % 89.12/12.54 --------------------------------- % 89.12/12.54 % 89.12/12.54 (mDefSImg) % 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 89.60/12.57 $i] : ( ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v5) = v4) | ~ % 89.60/12.57 (szDzozmdt0(v0) = v1) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 89.60/12.57 $i(v0) | ~ aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aElementOf0(v5, v2) % 89.60/12.57 | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 89.60/12.57 $i] : ! [v4: $i] : (v4 = v3 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ % 89.60/12.57 (szDzozmdt0(v0) = v1) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ % 89.60/12.57 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aSet0(v4) | ? [v5: $i] : ? % 89.60/12.57 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & ( ~ aElementOf0(v5, v4) | ! % 89.60/12.57 [v8: $i] : ( ~ (sdtlpdtrp0(v0, v8) = v5) | ~ $i(v8) | ~ % 89.60/12.57 aElementOf0(v8, v2))) & (aElementOf0(v5, v4) | (v7 = v5 & % 89.60/12.57 sdtlpdtrp0(v0, v6) = v5 & aElementOf0(v6, v2))))) & ! [v0: $i] : ! % 89.60/12.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlcdtrc0(v0, v2) = % 89.60/12.57 v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 89.60/12.57 $i(v0) | ~ aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aElementOf0(v4, v3) % 89.60/12.57 | ? [v5: $i] : (sdtlpdtrp0(v0, v5) = v4 & $i(v5) & aElementOf0(v5, v2))) & % 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0, v2) % 89.60/12.57 = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 89.60/12.57 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | aSet0(v3)) % 89.60/12.57 % 89.60/12.57 (mDefSub) % 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 89.60/12.57 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 89.60/12.57 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 89.60/12.57 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 89.60/12.57 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 89.60/12.57 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 89.60/12.57 % 89.60/12.57 (mNATSet) % 89.60/12.58 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 89.60/12.58 % 89.60/12.58 (m__) % 89.60/12.58 $i(xx) & $i(xd) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) | % 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)) % 89.60/12.58 % 89.60/12.58 (m__4730) % 89.60/12.58 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 89.60/12.58 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | % 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 89.60/12.58 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ % 89.60/12.58 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 89.60/12.58 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) % 89.60/12.58 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 89.60/12.58 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 89.60/12.58 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 89.60/12.58 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | % 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v4 & sdtlpdtrp0(xC, v0) = v5 % 89.60/12.58 & sdtlpdtrp0(xN, v1) = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) & % 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v4 | ~ % 89.60/12.58 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~ % 89.60/12.58 aSet0(v6)))) % 89.60/12.58 % 89.60/12.58 (m__4769) % 89.60/12.58 $i(xd) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) % 89.60/12.58 = v0 & $i(v1) & $i(v0) & aSet0(v1)) % 89.60/12.58 % 89.60/12.58 (m__4781) % 89.60/12.58 $i(xx) & $i(xd) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 89.60/12.58 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aElementOf0(xx, v1)) % 89.60/12.58 % 89.60/12.59 (function-axioms) % 89.60/12.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 89.60/12.59 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 89.60/12.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 89.60/12.59 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 89.60/12.59 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 89.60/12.59 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 89.60/12.59 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 89.60/12.59 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 89.60/12.59 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 89.60/12.59 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 89.60/12.59 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 89.60/12.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 89.60/12.59 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 89.60/12.59 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 89.60/12.59 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 89.60/12.59 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 89.60/12.59 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 89.60/12.59 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 89.60/12.59 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 89.60/12.59 v0)) % 89.60/12.59 % 89.60/12.59 Further assumptions not needed in the proof: % 89.60/12.59 -------------------------------------------- % 89.60/12.59 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 89.60/12.59 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 89.60/12.59 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSeg, % 89.60/12.59 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 89.60/12.59 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 89.60/12.59 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 89.60/12.59 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 89.60/12.59 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 89.60/12.59 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 89.60/12.59 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 89.60/12.59 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, % 89.60/12.59 m__4331, m__4411, m__4618, m__4660 % 89.60/12.59 % 89.60/12.59 Those formulas are unsatisfiable: % 89.60/12.59 --------------------------------- % 89.60/12.59 % 89.60/12.59 Begin of proof % 89.60/12.59 | % 89.60/12.59 | ALPHA: (mDefSub) implies: % 89.60/12.59 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 89.60/12.59 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 89.60/12.59 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 89.60/12.59 | % 89.60/12.59 | ALPHA: (mNATSet) implies: % 89.60/12.59 | (2) aSet0(szNzAzT0) % 89.60/12.59 | % 89.60/12.59 | ALPHA: (mDefSImg) implies: % 89.60/12.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 89.60/12.59 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v4) | % 89.60/12.59 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ aFunction0(v0) | ~ % 89.60/12.59 | aSubsetOf0(v2, v1) | ~ aElementOf0(v4, v3) | ? [v5: $i] : % 89.60/12.59 | (sdtlpdtrp0(v0, v5) = v4 & $i(v5) & aElementOf0(v5, v2))) % 89.60/12.59 | % 89.60/12.59 | ALPHA: (m__4730) implies: % 89.60/12.60 | (4) aFunction0(xd) % 89.60/12.60 | (5) szDzozmdt0(xd) = szNzAzT0 % 89.60/12.60 | % 89.60/12.60 | ALPHA: (m__4769) implies: % 89.60/12.60 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 89.60/12.60 | v0 & $i(v1) & $i(v0) & aSet0(v1)) % 89.60/12.60 | % 89.60/12.60 | ALPHA: (m__4781) implies: % 89.60/12.60 | (7) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 89.60/12.60 | v0 & $i(v1) & $i(v0) & aElementOf0(xx, v1)) % 89.60/12.60 | % 89.60/12.60 | ALPHA: (m__) implies: % 89.60/12.60 | (8) $i(xd) % 89.60/12.60 | (9) $i(xx) % 89.60/12.60 | (10) ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) | ~ $i(v0) | ~ % 89.60/12.60 | aElementOf0(v0, szNzAzT0)) % 89.60/12.60 | % 89.60/12.60 | ALPHA: (function-axioms) implies: % 89.60/12.60 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 89.60/12.60 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 89.60/12.60 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 89.60/12.60 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0)) % 89.60/12.60 | % 89.60/12.60 | DELTA: instantiating (6) with fresh symbols all_77_0, all_77_1 gives: % 89.60/12.60 | (13) sdtlcdtrc0(xd, all_77_1) = all_77_0 & szDzozmdt0(xd) = all_77_1 & % 89.60/12.60 | $i(all_77_0) & $i(all_77_1) & aSet0(all_77_0) % 89.60/12.60 | % 89.60/12.60 | ALPHA: (13) implies: % 89.60/12.60 | (14) $i(all_77_1) % 89.60/12.60 | (15) szDzozmdt0(xd) = all_77_1 % 89.60/12.60 | (16) sdtlcdtrc0(xd, all_77_1) = all_77_0 % 89.60/12.60 | % 89.60/12.60 | DELTA: instantiating (7) with fresh symbols all_79_0, all_79_1 gives: % 89.60/12.60 | (17) sdtlcdtrc0(xd, all_79_1) = all_79_0 & szDzozmdt0(xd) = all_79_1 & % 89.60/12.60 | $i(all_79_0) & $i(all_79_1) & aElementOf0(xx, all_79_0) % 89.60/12.60 | % 89.60/12.60 | ALPHA: (17) implies: % 89.60/12.60 | (18) aElementOf0(xx, all_79_0) % 89.60/12.60 | (19) $i(all_79_0) % 89.60/12.60 | (20) szDzozmdt0(xd) = all_79_1 % 89.60/12.60 | (21) sdtlcdtrc0(xd, all_79_1) = all_79_0 % 89.60/12.60 | % 89.60/12.60 | GROUND_INST: instantiating (11) with all_77_1, all_79_1, xd, simplifying with % 89.60/12.60 | (15), (20) gives: % 89.60/12.60 | (22) all_79_1 = all_77_1 % 89.60/12.60 | % 89.60/12.60 | GROUND_INST: instantiating (11) with szNzAzT0, all_79_1, xd, simplifying with % 89.60/12.60 | (5), (20) gives: % 89.60/12.60 | (23) all_79_1 = szNzAzT0 % 89.60/12.60 | % 89.60/12.60 | GROUND_INST: instantiating (12) with all_77_0, all_79_0, all_77_1, xd, % 89.60/12.60 | simplifying with (16) gives: % 89.60/12.60 | (24) all_79_0 = all_77_0 | ~ (sdtlcdtrc0(xd, all_77_1) = all_79_0) % 89.60/12.60 | % 89.60/12.60 | COMBINE_EQS: (22), (23) imply: % 89.60/12.60 | (25) all_77_1 = szNzAzT0 % 89.60/12.60 | % 89.60/12.60 | SIMP: (25) implies: % 89.60/12.60 | (26) all_77_1 = szNzAzT0 % 89.60/12.60 | % 89.60/12.60 | REDUCE: (21), (23) imply: % 89.60/12.60 | (27) sdtlcdtrc0(xd, szNzAzT0) = all_79_0 % 89.60/12.60 | % 89.60/12.60 | REDUCE: (14), (26) imply: % 89.60/12.60 | (28) $i(szNzAzT0) % 89.60/12.60 | % 89.60/12.60 | BETA: splitting (24) gives: % 89.60/12.60 | % 89.60/12.60 | Case 1: % 89.60/12.60 | | % 89.60/12.60 | | (29) ~ (sdtlcdtrc0(xd, all_77_1) = all_79_0) % 89.60/12.60 | | % 89.60/12.61 | | REDUCE: (26), (29) imply: % 89.60/12.61 | | (30) ~ (sdtlcdtrc0(xd, szNzAzT0) = all_79_0) % 89.60/12.61 | | % 89.60/12.61 | | PRED_UNIFY: (27), (30) imply: % 89.60/12.61 | | (31) $false % 89.60/12.61 | | % 89.60/12.61 | | CLOSE: (31) is inconsistent. % 89.60/12.61 | | % 89.60/12.61 | Case 2: % 89.60/12.61 | | % 89.60/12.61 | | (32) all_79_0 = all_77_0 % 89.60/12.61 | | % 89.60/12.61 | | REDUCE: (27), (32) imply: % 89.60/12.61 | | (33) sdtlcdtrc0(xd, szNzAzT0) = all_77_0 % 89.60/12.61 | | % 89.60/12.61 | | REDUCE: (19), (32) imply: % 89.60/12.61 | | (34) $i(all_77_0) % 89.60/12.61 | | % 89.60/12.61 | | REDUCE: (18), (32) imply: % 89.60/12.61 | | (35) aElementOf0(xx, all_77_0) % 89.60/12.61 | | % 89.60/12.61 | | GROUND_INST: instantiating (1) with szNzAzT0, szNzAzT0, simplifying with % 89.60/12.61 | | (2), (28) gives: % 89.60/12.61 | | (36) aSubsetOf0(szNzAzT0, szNzAzT0) % 89.60/12.61 | | % 89.60/12.61 | | GROUND_INST: instantiating (3) with xd, szNzAzT0, szNzAzT0, all_77_0, xx, % 89.60/12.61 | | simplifying with (4), (5), (8), (9), (28), (33), (34), (35) % 89.81/12.61 | | gives: % 89.81/12.61 | | (37) ~ aSubsetOf0(szNzAzT0, szNzAzT0) | ? [v0: $i] : (sdtlpdtrp0(xd, % 89.81/12.61 | | v0) = xx & $i(v0) & aElementOf0(v0, szNzAzT0)) % 89.81/12.61 | | % 89.81/12.61 | | BETA: splitting (37) gives: % 89.81/12.61 | | % 89.81/12.61 | | Case 1: % 89.81/12.61 | | | % 89.81/12.61 | | | (38) ~ aSubsetOf0(szNzAzT0, szNzAzT0) % 89.81/12.61 | | | % 89.81/12.61 | | | PRED_UNIFY: (36), (38) imply: % 89.81/12.61 | | | (39) $false % 89.81/12.61 | | | % 89.81/12.61 | | | CLOSE: (39) is inconsistent. % 89.81/12.61 | | | % 89.81/12.61 | | Case 2: % 89.81/12.61 | | | % 89.81/12.61 | | | (40) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = xx & $i(v0) & aElementOf0(v0, % 89.81/12.61 | | | szNzAzT0)) % 89.81/12.61 | | | % 89.81/12.61 | | | DELTA: instantiating (40) with fresh symbol all_156_0 gives: % 89.81/12.61 | | | (41) sdtlpdtrp0(xd, all_156_0) = xx & $i(all_156_0) & % 89.81/12.61 | | | aElementOf0(all_156_0, szNzAzT0) % 89.81/12.61 | | | % 89.81/12.61 | | | ALPHA: (41) implies: % 89.81/12.61 | | | (42) aElementOf0(all_156_0, szNzAzT0) % 89.81/12.61 | | | (43) $i(all_156_0) % 89.81/12.61 | | | (44) sdtlpdtrp0(xd, all_156_0) = xx % 89.81/12.61 | | | % 89.81/12.61 | | | GROUND_INST: instantiating (10) with all_156_0, simplifying with (42), % 89.81/12.61 | | | (43), (44) gives: % 89.81/12.61 | | | (45) $false % 89.81/12.61 | | | % 89.81/12.61 | | | CLOSE: (45) is inconsistent. % 89.81/12.61 | | | % 89.81/12.61 | | End of split % 89.81/12.61 | | % 89.81/12.61 | End of split % 89.81/12.61 | % 89.81/12.61 End of proof % 89.81/12.61 % SZS output end Proof for theBenchmark % 89.81/12.61 % 89.81/12.61 12009ms %------------------------------------------------------------------------------