%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM618+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 : n011.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 26.80s 4.39s % Output : Proof 53.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM618+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n011.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 17:02:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.25/1.65 Prover 1: Preprocessing ... % 6.25/1.67 Prover 4: Preprocessing ... % 6.85/1.72 Prover 0: Preprocessing ... % 6.85/1.72 Prover 3: Preprocessing ... % 6.85/1.72 Prover 6: Preprocessing ... % 6.85/1.72 Prover 5: Preprocessing ... % 6.85/1.72 Prover 2: Preprocessing ... % 18.95/3.36 Prover 3: Constructing countermodel ... % 18.95/3.36 Prover 6: Proving ... % 18.95/3.38 Prover 1: Constructing countermodel ... % 21.82/3.75 Prover 5: Proving ... % 26.80/4.39 Prover 3: proved (3755ms) % 26.80/4.39 % 26.80/4.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.80/4.39 % 26.80/4.39 Prover 5: stopped % 26.80/4.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.80/4.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.80/4.39 Prover 6: stopped % 26.80/4.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 28.77/4.69 Prover 10: Preprocessing ... % 29.33/4.71 Prover 8: Preprocessing ... % 29.83/4.77 Prover 7: Preprocessing ... % 32.90/5.26 Prover 8: Warning: ignoring some quantifiers % 33.52/5.27 Prover 8: Constructing countermodel ... % 35.40/5.56 Prover 10: Constructing countermodel ... % 39.36/6.03 Prover 7: Constructing countermodel ... % 45.84/6.85 Prover 4: Constructing countermodel ... % 50.72/7.49 Prover 2: Proving ... % 50.72/7.52 Prover 2: stopped % 50.72/7.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 50.72/7.52 Prover 10: Found proof (size 25) % 50.72/7.52 Prover 10: proved (3124ms) % 50.72/7.52 Prover 4: stopped % 50.72/7.52 Prover 7: stopped % 50.72/7.53 Prover 8: stopped % 51.09/7.54 Prover 1: stopped % 52.06/7.74 Prover 11: Preprocessing ... % 53.18/7.94 Prover 11: stopped % 53.39/8.01 Prover 0: Proving ... % 53.39/8.04 Prover 0: stopped % 53.39/8.04 % 53.39/8.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 53.39/8.04 % 53.39/8.04 % SZS output start Proof for theBenchmark % 53.65/8.05 Assumptions after simplification: % 53.65/8.05 --------------------------------- % 53.65/8.05 % 53.65/8.05 (mCountNFin_01) % 53.65/8.06 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 53.65/8.06 % 53.65/8.06 (mDefEmp) % 53.65/8.06 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 53.65/8.06 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 53.65/8.06 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 53.71/8.06 % 53.71/8.06 (mDefSub) % 53.71/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 53.71/8.07 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 53.71/8.07 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 53.71/8.07 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 53.71/8.07 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 53.71/8.07 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 53.71/8.07 % 53.71/8.07 (m__) % 53.71/8.09 $i(xx) & $i(xe) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) | % 53.71/8.09 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)) % 53.71/8.09 % 53.71/8.09 (m__4891) % 53.71/8.10 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 53.71/8.10 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 53.71/8.10 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 53.71/8.10 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 53.71/8.10 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 53.71/8.10 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 53.71/8.10 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 53.71/8.10 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 53.71/8.10 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 53.71/8.10 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 53.71/8.10 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 53.71/8.10 aElementOf0(v4, v1)))) % 53.71/8.10 % 53.71/8.10 (m__4982) % 53.71/8.10 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 53.71/8.10 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 53.71/8.10 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 53.71/8.10 aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 & % 53.71/8.10 sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & aElementOf0(v4, % 53.71/8.10 szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? % 53.71/8.10 [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & sdtlpdtrp0(xe, v3) = v2 & $i(v3) & % 53.71/8.10 aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 53.71/8.10 % 53.71/8.10 (m__5208) % 53.71/8.10 $i(xP) & $i(xO) & aSubsetOf0(xP, xO) & ! [v0: $i] : ( ~ $i(v0) | ~ % 53.71/8.10 aElementOf0(v0, xP) | aElementOf0(v0, xO)) % 53.71/8.10 % 53.71/8.10 (m__5270) % 53.71/8.10 $i(xP) & $i(xO) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xO, xk) = v0 & $i(v0) & % 53.71/8.10 aElementOf0(xP, v0)) % 53.71/8.10 % 53.71/8.10 (m__5348) % 53.71/8.11 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & % 53.71/8.11 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 53.71/8.11 % 53.71/8.11 Further assumptions not needed in the proof: % 53.71/8.11 -------------------------------------------- % 53.71/8.11 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 53.71/8.11 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 53.71/8.11 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 53.71/8.11 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 53.71/8.11 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 53.71/8.11 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 53.71/8.11 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 53.71/8.11 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 53.71/8.11 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 53.71/8.11 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 53.71/8.11 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, % 53.71/8.11 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4908, m__4998, % 53.71/8.11 m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173, m__5182, m__5195, % 53.71/8.11 m__5217, m__5309, m__5321, m__5365 % 53.71/8.11 % 53.71/8.11 Those formulas are unsatisfiable: % 53.71/8.11 --------------------------------- % 53.71/8.11 % 53.71/8.11 Begin of proof % 53.71/8.11 | % 53.71/8.11 | ALPHA: (mDefEmp) implies: % 53.71/8.11 | (1) aSet0(slcrc0) % 53.71/8.11 | % 53.71/8.11 | ALPHA: (mCountNFin_01) implies: % 53.71/8.11 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 53.71/8.11 | % 53.71/8.11 | ALPHA: (mDefSub) implies: % 53.71/8.11 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 53.71/8.11 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 53.71/8.11 | aSet0(v0) | aElementOf0(v2, v0)) % 53.71/8.11 | % 53.71/8.11 | ALPHA: (m__4891) implies: % 53.95/8.11 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 53.95/8.11 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 53.95/8.11 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 53.95/8.11 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 53.95/8.11 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 53.95/8.11 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 53.95/8.11 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 53.95/8.11 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 53.95/8.11 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 53.95/8.11 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 53.95/8.11 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 53.95/8.11 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 53.95/8.11 | $i(v4) & aElementOf0(v4, v1)))) % 53.95/8.11 | % 53.95/8.11 | ALPHA: (m__4982) implies: % 53.95/8.11 | (5) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 53.95/8.11 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 53.95/8.11 | (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 53.95/8.11 | aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 & % 53.95/8.12 | sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & % 53.95/8.12 | aElementOf0(v4, szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 53.95/8.12 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & % 53.95/8.12 | sdtlpdtrp0(xe, v3) = v2 & $i(v3) & aElementOf0(v3, v1) & % 53.95/8.12 | aElementOf0(v3, szNzAzT0)))) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (m__5208) implies: % 53.95/8.12 | (6) aSubsetOf0(xP, xO) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (m__5270) implies: % 53.95/8.12 | (7) $i(xO) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (m__5348) implies: % 53.95/8.12 | (8) $i(xP) % 53.95/8.12 | (9) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) & % 53.95/8.12 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (m__) implies: % 53.95/8.12 | (10) $i(xx) % 53.95/8.12 | (11) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) | ~ $i(v0) | ~ % 53.95/8.12 | aElementOf0(v0, szNzAzT0)) % 53.95/8.12 | % 53.95/8.12 | DELTA: instantiating (9) with fresh symbol all_87_0 gives: % 53.95/8.12 | (12) ~ (all_87_0 = xx) & szmzizndt0(xQ) = all_87_0 & $i(all_87_0) & % 53.95/8.12 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (12) implies: % 53.95/8.12 | (13) aElementOf0(xx, xP) % 53.95/8.12 | % 53.95/8.12 | DELTA: instantiating (5) with fresh symbols all_113_0, all_113_1 gives: % 53.95/8.12 | (14) szDzizrdt0(xd) = all_113_1 & sdtlbdtrb0(xd, all_113_1) = all_113_0 & % 53.95/8.12 | $i(all_113_0) & $i(all_113_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 53.95/8.12 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 53.95/8.12 | aElementOf0(v1, all_113_0) | ? [v2: $i] : (sdtlpdtrp0(xd, v2) = % 53.95/8.12 | all_113_1 & sdtlpdtrp0(xe, v2) = v0 & $i(v2) & aElementOf0(v2, % 53.95/8.12 | all_113_0) & aElementOf0(v2, szNzAzT0))) & ! [v0: $i] : ( ~ % 53.95/8.12 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xd, v1) % 53.95/8.12 | = all_113_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, % 53.95/8.12 | all_113_0) & aElementOf0(v1, szNzAzT0))) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (14) implies: % 53.95/8.12 | (15) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : % 53.95/8.12 | (sdtlpdtrp0(xd, v1) = all_113_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & % 53.95/8.12 | aElementOf0(v1, all_113_0) & aElementOf0(v1, szNzAzT0))) % 53.95/8.12 | % 53.95/8.12 | DELTA: instantiating (4) with fresh symbols all_116_0, all_116_1, all_116_2 % 53.95/8.12 | gives: % 53.95/8.12 | (16) szDzizrdt0(xd) = all_116_2 & sdtlcdtrc0(xe, all_116_1) = xO & % 53.95/8.12 | sdtlbdtrb0(xd, all_116_2) = all_116_1 & szDzozmdt0(xd) = all_116_0 & % 53.95/8.12 | $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & aSet0(all_116_1) & % 53.95/8.12 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_116_2 | ~ % 53.95/8.12 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 53.95/8.12 | all_116_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 53.95/8.12 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_116_1) | % 53.95/8.12 | aElementOf0(v0, all_116_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 53.95/8.12 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 53.95/8.12 | aElementOf0(v1, all_116_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 53.95/8.12 | ~ (sdtlpdtrp0(xd, v0) = all_116_2) | ~ $i(v0) | ~ aElementOf0(v0, % 53.95/8.12 | all_116_0) | aElementOf0(v0, all_116_1)) & ! [v0: $i] : ( ~ % 53.95/8.12 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 53.95/8.12 | = v0 & $i(v1) & aElementOf0(v1, all_116_1))) % 53.95/8.12 | % 53.95/8.12 | ALPHA: (16) implies: % 53.95/8.12 | (17) aSet0(xO) % 53.95/8.12 | % 53.95/8.12 | BETA: splitting (2) gives: % 53.95/8.12 | % 53.95/8.13 | Case 1: % 53.95/8.13 | | % 53.95/8.13 | | (18) ~ aSet0(slcrc0) % 53.95/8.13 | | % 53.95/8.13 | | PRED_UNIFY: (1), (18) imply: % 53.95/8.13 | | (19) $false % 53.95/8.13 | | % 53.95/8.13 | | CLOSE: (19) is inconsistent. % 53.95/8.13 | | % 53.95/8.13 | Case 2: % 53.95/8.13 | | % 53.95/8.13 | | % 53.95/8.13 | | GROUND_INST: instantiating (3) with xO, xP, xx, simplifying with (6), (7), % 53.95/8.13 | | (8), (10), (13), (17) gives: % 53.95/8.13 | | (20) aElementOf0(xx, xO) % 53.95/8.13 | | % 53.95/8.13 | | GROUND_INST: instantiating (15) with xx, simplifying with (10), (20) gives: % 53.95/8.13 | | (21) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = all_113_1 & sdtlpdtrp0(xe, v0) = % 53.95/8.13 | | xx & $i(v0) & aElementOf0(v0, all_113_0) & aElementOf0(v0, % 53.95/8.13 | | szNzAzT0)) % 53.95/8.13 | | % 53.95/8.13 | | DELTA: instantiating (21) with fresh symbol all_226_0 gives: % 53.95/8.13 | | (22) sdtlpdtrp0(xd, all_226_0) = all_113_1 & sdtlpdtrp0(xe, all_226_0) = % 53.95/8.13 | | xx & $i(all_226_0) & aElementOf0(all_226_0, all_113_0) & % 53.95/8.13 | | aElementOf0(all_226_0, szNzAzT0) % 53.95/8.13 | | % 53.95/8.13 | | ALPHA: (22) implies: % 53.95/8.13 | | (23) aElementOf0(all_226_0, szNzAzT0) % 53.95/8.13 | | (24) $i(all_226_0) % 53.95/8.13 | | (25) sdtlpdtrp0(xe, all_226_0) = xx % 53.95/8.13 | | % 53.95/8.13 | | GROUND_INST: instantiating (11) with all_226_0, simplifying with (23), (24), % 53.95/8.13 | | (25) gives: % 53.95/8.13 | | (26) $false % 53.95/8.13 | | % 53.95/8.13 | | CLOSE: (26) is inconsistent. % 53.95/8.13 | | % 53.95/8.13 | End of split % 53.95/8.13 | % 53.95/8.13 End of proof % 53.95/8.13 % SZS output end Proof for theBenchmark % 53.95/8.13 % 53.95/8.13 7519ms %------------------------------------------------------------------------------