%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM558+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 : n018.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 11:48:36 EDT 2023 % Result : Theorem 87.42s 12.42s % Output : Proof 88.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM558+3 : 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 : n018.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 18:01:44 EDT 2023 % 0.19/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 4.33/1.36 Prover 4: Preprocessing ... % 4.33/1.36 Prover 1: Preprocessing ... % 4.33/1.42 Prover 2: Preprocessing ... % 4.33/1.42 Prover 6: Preprocessing ... % 4.33/1.43 Prover 5: Preprocessing ... % 4.33/1.43 Prover 0: Preprocessing ... % 4.33/1.45 Prover 3: Preprocessing ... % 13.53/2.61 Prover 1: Constructing countermodel ... % 14.64/2.77 Prover 3: Constructing countermodel ... % 14.64/2.84 Prover 6: Proving ... % 14.64/2.85 Prover 5: Proving ... % 14.64/2.86 Prover 2: Proving ... % 19.05/3.42 Prover 4: Constructing countermodel ... % 20.17/3.62 Prover 0: Proving ... % 70.94/10.29 Prover 2: stopped % 70.94/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.69/10.38 Prover 7: Preprocessing ... % 73.25/10.62 Prover 7: Constructing countermodel ... % 87.42/12.40 Prover 7: Found proof (size 37) % 87.42/12.41 Prover 7: proved (2117ms) % 87.42/12.41 Prover 5: stopped % 87.42/12.41 Prover 0: stopped % 87.42/12.41 Prover 6: stopped % 87.42/12.41 Prover 3: stopped % 87.42/12.41 Prover 1: stopped % 87.42/12.42 Prover 4: stopped % 87.42/12.42 % 87.42/12.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 87.42/12.42 % 87.42/12.42 % SZS output start Proof for theBenchmark % 87.42/12.43 Assumptions after simplification: % 87.42/12.43 --------------------------------- % 87.42/12.43 % 87.42/12.43 (mDefSub) % 87.42/12.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 87.42/12.44 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 87.42/12.44 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 87.42/12.44 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 87.42/12.44 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 87.42/12.44 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 87.42/12.44 % 87.42/12.44 (mEOfElem) % 87.42/12.44 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 87.42/12.44 ~ aSet0(v0) | aElement0(v1)) % 87.42/12.44 % 87.42/12.44 (m__) % 87.42/12.44 $i(xx) & $i(xT) & ~ aElementOf0(xx, xT) % 87.42/12.44 % 87.42/12.44 (m__2202_02) % 87.71/12.44 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS) % 87.71/12.44 % 87.71/12.44 (m__2227) % 87.75/12.47 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 87.75/12.47 $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = % 87.75/12.47 v0 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & aElementOf0(v2, v0) & % 87.75/12.47 aSet0(v1) & aSet0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 87.75/12.47 (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v3) | ~ % 87.75/12.47 aElementOf0(v3, v1) | aElementOf0(v5, xT)) & ! [v3: $i] : ! [v4: $i] : % 87.75/12.47 ! [v5: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 87.75/12.47 aElementOf0(v5, v3) | ~ aElementOf0(v3, v0) | aElementOf0(v5, xS)) & ! % 87.75/12.47 [v3: $i] : ! [v4: $i] : (v4 = xk | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ % 87.75/12.47 aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : (v4 = xk | ~ % 87.75/12.47 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0)) & ! [v3: $i] : % 87.75/12.47 ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 87.75/12.47 aSubsetOf0(v3, xT)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) % 87.75/12.47 | ~ $i(v3) | ~ aElementOf0(v3, v1) | aSet0(v3)) & ! [v3: $i] : ! [v4: % 87.75/12.47 $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) | % 87.75/12.47 aSubsetOf0(v3, xS)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) % 87.75/12.47 | ~ $i(v3) | ~ aElementOf0(v3, v0) | aSet0(v3)) & ! [v3: $i] : ( ~ % 87.75/12.47 (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSubsetOf0(v3, xT) | aElementOf0(v3, % 87.75/12.47 v1)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ % 87.75/12.47 aSubsetOf0(v3, xS) | aElementOf0(v3, v0)) & ! [v3: $i] : ( ~ % 87.75/12.47 (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | aElementOf0(v3, v1) | ? % 87.75/12.47 [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ aElementOf0(v4, xT))) & ! % 87.75/12.47 [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | % 87.75/12.47 aElementOf0(v3, v0) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ % 87.75/12.47 aElementOf0(v4, xS))) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, % 87.75/12.47 v0) | aElementOf0(v3, v1))) % 87.75/12.47 % 87.75/12.47 (m__2256) % 87.75/12.47 $i(xx) & $i(xS) & aElementOf0(xx, xS) % 87.75/12.47 % 87.75/12.47 (m__2270) % 87.75/12.47 $i(xQ) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & % 87.75/12.47 sbrdtbr0(xQ) = xk & $i(v0) & aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & % 87.75/12.47 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 87.75/12.47 aElementOf0(v1, xS))) % 87.75/12.47 % 87.75/12.47 (m__2357) % 87.75/12.47 $i(xP) & $i(xy) & $i(xQ) & $i(xx) & ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & % 87.75/12.47 sdtpldt0(v0, xx) = xP & $i(v0) & aSet0(v0) & aSet0(xP) & ~ aElementOf0(xy, % 87.75/12.47 v0) & ! [v1: $i] : (v1 = xy | ~ $i(v1) | ~ aElementOf0(v1, xQ) | ~ % 87.75/12.47 aElement0(v1) | aElementOf0(v1, v0)) & ! [v1: $i] : (v1 = xx | ~ $i(v1) % 87.75/12.47 | ~ aElementOf0(v1, xP) | aElementOf0(v1, v0)) & ! [v1: $i] : ( ~ $i(v1) % 87.75/12.47 | ~ aElementOf0(v1, v0) | ~ aElement0(v1) | aElementOf0(v1, xP)) & ! % 87.75/12.47 [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | aElementOf0(v1, xQ)) & ! % 87.75/12.47 [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | aElement0(v1)) & ! [v1: % 87.75/12.47 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ( ~ % 87.75/12.47 aElement0(xx) | aElementOf0(xx, xP))) % 87.75/12.47 % 87.75/12.47 (m__2378) % 87.75/12.47 $i(xP) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & % 87.75/12.47 sbrdtbr0(xP) = xk & $i(v0) & aSubsetOf0(xP, xS) & aElementOf0(xP, v0) & ! % 87.75/12.47 [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xS))) % 87.75/12.47 % 87.75/12.47 (function-axioms) % 87.75/12.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.75/12.48 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] % 87.75/12.48 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = % 87.75/12.48 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 87.75/12.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 87.75/12.48 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 87.75/12.48 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 87.75/12.48 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & % 87.75/12.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) % 87.75/12.48 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 87.75/12.48 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 87.75/12.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 87.75/12.48 (szszuzczcdt0(v2) = v0)) % 87.75/12.48 % 87.75/12.48 Further assumptions not needed in the proof: % 87.75/12.48 -------------------------------------------- % 87.75/12.48 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 87.75/12.48 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 87.75/12.48 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDiffCons, % 87.75/12.48 mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, % 87.75/12.48 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, % 87.75/12.48 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, % 87.75/12.48 mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, mSubRefl, % 87.75/12.48 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__2202, % 87.75/12.48 m__2291, m__2304, m__2323, m__2338 % 87.75/12.48 % 87.75/12.48 Those formulas are unsatisfiable: % 87.75/12.48 --------------------------------- % 87.75/12.48 % 87.75/12.48 Begin of proof % 87.75/12.48 | % 87.75/12.48 | ALPHA: (mDefSub) implies: % 87.75/12.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 87.75/12.48 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 87.75/12.48 | aSet0(v0) | aElementOf0(v2, v0)) % 87.75/12.48 | % 87.75/12.48 | ALPHA: (m__2202_02) implies: % 87.75/12.48 | (2) aSet0(xS) % 87.75/12.48 | (3) aSet0(xT) % 87.75/12.48 | % 87.75/12.48 | ALPHA: (m__2227) implies: % 87.75/12.48 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = slcrc0) & % 87.75/12.48 | slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v2) & % 87.75/12.48 | $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & aElementOf0(v2, v0) & % 87.75/12.48 | aSet0(v1) & aSet0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 87.75/12.48 | (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, % 87.75/12.48 | v3) | ~ aElementOf0(v3, v1) | aElementOf0(v5, xT)) & ! [v3: $i] % 87.75/12.48 | : ! [v4: $i] : ! [v5: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v5) | % 87.75/12.48 | ~ $i(v3) | ~ aElementOf0(v5, v3) | ~ aElementOf0(v3, v0) | % 87.75/12.48 | aElementOf0(v5, xS)) & ! [v3: $i] : ! [v4: $i] : (v4 = xk | ~ % 87.75/12.48 | (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & ! [v3: % 87.75/12.48 | $i] : ! [v4: $i] : (v4 = xk | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | % 87.75/12.48 | ~ aElementOf0(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 87.75/12.48 | (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 87.75/12.48 | aSubsetOf0(v3, xT)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) % 87.75/12.48 | = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | aSet0(v3)) & ! [v3: % 87.75/12.48 | $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ % 87.75/12.48 | aElementOf0(v3, v0) | aSubsetOf0(v3, xS)) & ! [v3: $i] : ! [v4: % 87.75/12.49 | $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) % 87.75/12.49 | | aSet0(v3)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | % 87.75/12.49 | ~ aSubsetOf0(v3, xT) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ % 87.75/12.49 | (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSubsetOf0(v3, xS) | % 87.75/12.49 | aElementOf0(v3, v0)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ % 87.75/12.49 | $i(v3) | ~ aSet0(v3) | aElementOf0(v3, v1) | ? [v4: $i] : ($i(v4) % 87.75/12.49 | & aElementOf0(v4, v3) & ~ aElementOf0(v4, xT))) & ! [v3: $i] : % 87.75/12.49 | ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | aElementOf0(v3, % 87.75/12.49 | v0) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ % 87.75/12.49 | aElementOf0(v4, xS))) & ! [v3: $i] : ( ~ $i(v3) | ~ % 87.75/12.49 | aElementOf0(v3, v0) | aElementOf0(v3, v1))) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (m__2256) implies: % 87.75/12.49 | (5) aElementOf0(xx, xS) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (m__2270) implies: % 87.75/12.49 | (6) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & sbrdtbr0(xQ) = xk & $i(v0) & % 87.75/12.49 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 87.75/12.49 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xS))) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (m__2357) implies: % 87.75/12.49 | (7) ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & sdtpldt0(v0, xx) = xP & $i(v0) & % 87.75/12.49 | aSet0(v0) & aSet0(xP) & ~ aElementOf0(xy, v0) & ! [v1: $i] : (v1 = % 87.75/12.49 | xy | ~ $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 87.75/12.49 | aElementOf0(v1, v0)) & ! [v1: $i] : (v1 = xx | ~ $i(v1) | ~ % 87.75/12.49 | aElementOf0(v1, xP) | aElementOf0(v1, v0)) & ! [v1: $i] : ( ~ % 87.75/12.49 | $i(v1) | ~ aElementOf0(v1, v0) | ~ aElement0(v1) | % 87.75/12.49 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 87.75/12.49 | aElementOf0(v1, v0) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 87.75/12.49 | $i(v1) | ~ aElementOf0(v1, v0) | aElement0(v1)) & ! [v1: $i] : ( % 87.75/12.49 | ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ( ~ % 87.75/12.49 | aElement0(xx) | aElementOf0(xx, xP))) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (m__2378) implies: % 87.75/12.49 | (8) $i(xS) % 87.75/12.49 | (9) $i(xP) % 87.75/12.49 | (10) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & sbrdtbr0(xP) = xk & $i(v0) % 87.75/12.49 | & aSubsetOf0(xP, xS) & aElementOf0(xP, v0) & ! [v1: $i] : ( ~ % 87.75/12.49 | $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xS))) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (m__) implies: % 87.75/12.49 | (11) ~ aElementOf0(xx, xT) % 87.75/12.49 | (12) $i(xT) % 87.75/12.49 | (13) $i(xx) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (function-axioms) implies: % 87.75/12.49 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.75/12.49 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) % 87.75/12.49 | % 87.75/12.49 | DELTA: instantiating (10) with fresh symbol all_53_0 gives: % 87.75/12.49 | (15) slbdtsldtrb0(xS, xk) = all_53_0 & sbrdtbr0(xP) = xk & $i(all_53_0) & % 87.75/12.49 | aSubsetOf0(xP, xS) & aElementOf0(xP, all_53_0) & ! [v0: $i] : ( ~ % 87.75/12.49 | $i(v0) | ~ aElementOf0(v0, xP) | aElementOf0(v0, xS)) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (15) implies: % 87.75/12.49 | (16) aElementOf0(xP, all_53_0) % 87.75/12.49 | (17) sbrdtbr0(xP) = xk % 87.75/12.49 | (18) slbdtsldtrb0(xS, xk) = all_53_0 % 87.75/12.49 | % 87.75/12.49 | DELTA: instantiating (6) with fresh symbol all_56_0 gives: % 87.75/12.49 | (19) slbdtsldtrb0(xS, xk) = all_56_0 & sbrdtbr0(xQ) = xk & $i(all_56_0) & % 87.75/12.49 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, all_56_0) & aSet0(xQ) & ! [v0: % 87.75/12.49 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xS)) % 87.75/12.49 | % 87.75/12.49 | ALPHA: (19) implies: % 87.75/12.49 | (20) $i(all_56_0) % 87.75/12.49 | (21) slbdtsldtrb0(xS, xk) = all_56_0 % 87.75/12.49 | % 87.75/12.49 | DELTA: instantiating (7) with fresh symbol all_59_0 gives: % 87.75/12.50 | (22) sdtmndt0(xQ, xy) = all_59_0 & sdtpldt0(all_59_0, xx) = xP & % 87.75/12.50 | $i(all_59_0) & aSet0(all_59_0) & aSet0(xP) & ~ aElementOf0(xy, % 87.75/12.50 | all_59_0) & ! [v0: $i] : (v0 = xy | ~ $i(v0) | ~ aElementOf0(v0, % 87.75/12.50 | xQ) | ~ aElement0(v0) | aElementOf0(v0, all_59_0)) & ! [v0: $i] % 87.75/12.50 | : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0, xP) | aElementOf0(v0, % 87.75/12.50 | all_59_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 87.75/12.50 | all_59_0) | ~ aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] % 87.75/12.50 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_59_0) | aElementOf0(v0, xQ)) & % 87.75/12.50 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_59_0) | % 87.75/12.50 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xP) | % 87.75/12.50 | aElement0(v0)) & ( ~ aElement0(xx) | aElementOf0(xx, xP)) % 87.75/12.50 | % 87.75/12.50 | ALPHA: (22) implies: % 87.75/12.50 | (23) ~ aElement0(xx) | aElementOf0(xx, xP) % 87.75/12.50 | % 87.75/12.50 | DELTA: instantiating (4) with fresh symbols all_62_0, all_62_1, all_62_2 % 87.75/12.50 | gives: % 87.75/12.50 | (24) ~ (all_62_2 = slcrc0) & slbdtsldtrb0(xT, xk) = all_62_1 & % 87.75/12.50 | slbdtsldtrb0(xS, xk) = all_62_2 & $i(all_62_0) & $i(all_62_1) & % 87.75/12.50 | $i(all_62_2) & aSubsetOf0(all_62_2, all_62_1) & aElementOf0(all_62_0, % 87.75/12.50 | all_62_2) & aSet0(all_62_1) & aSet0(all_62_2) & ! [v0: $i] : ! % 87.75/12.50 | [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ % 87.75/12.50 | $i(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v0, all_62_1) | % 87.75/12.50 | aElementOf0(v2, xT)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 87.75/12.50 | (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v0) % 87.75/12.50 | | ~ aElementOf0(v0, all_62_2) | aElementOf0(v2, xS)) & ! [v0: $i] % 87.75/12.50 | : ! [v1: $i] : (v1 = xk | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 87.75/12.50 | aElementOf0(v0, all_62_1)) & ! [v0: $i] : ! [v1: $i] : (v1 = xk | % 87.75/12.50 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_62_2)) & % 87.75/12.50 | ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 87.75/12.50 | aElementOf0(v0, all_62_1) | aSubsetOf0(v0, xT)) & ! [v0: $i] : ! % 87.75/12.50 | [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 87.75/12.50 | all_62_1) | aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 87.75/12.50 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_62_2) | % 87.75/12.50 | aSubsetOf0(v0, xS)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) % 87.75/12.50 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_62_2) | aSet0(v0)) & ! % 87.75/12.50 | [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSubsetOf0(v0, xT) % 87.75/12.50 | | aElementOf0(v0, all_62_1)) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) % 87.75/12.50 | | ~ $i(v0) | ~ aSubsetOf0(v0, xS) | aElementOf0(v0, all_62_2)) & % 87.75/12.50 | ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSet0(v0) | % 87.75/12.50 | aElementOf0(v0, all_62_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, % 87.75/12.50 | v0) & ~ aElementOf0(v1, xT))) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) % 87.75/12.50 | = xk) | ~ $i(v0) | ~ aSet0(v0) | aElementOf0(v0, all_62_2) | ? % 87.75/12.50 | [v1: $i] : ($i(v1) & aElementOf0(v1, v0) & ~ aElementOf0(v1, xS))) % 87.75/12.50 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_62_2) | % 87.75/12.50 | aElementOf0(v0, all_62_1)) % 87.75/12.50 | % 87.75/12.50 | ALPHA: (24) implies: % 87.75/12.50 | (25) aSet0(all_62_1) % 87.75/12.50 | (26) aSubsetOf0(all_62_2, all_62_1) % 87.75/12.50 | (27) $i(all_62_1) % 87.75/12.50 | (28) slbdtsldtrb0(xS, xk) = all_62_2 % 87.75/12.50 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 87.75/12.50 | aElementOf0(v0, all_62_1) | aSubsetOf0(v0, xT)) % 87.75/12.50 | % 88.02/12.51 | GROUND_INST: instantiating (14) with all_56_0, all_62_2, xk, xS, simplifying % 88.02/12.51 | with (21), (28) gives: % 88.02/12.51 | (30) all_62_2 = all_56_0 % 88.02/12.51 | % 88.02/12.51 | GROUND_INST: instantiating (14) with all_53_0, all_62_2, xk, xS, simplifying % 88.02/12.51 | with (18), (28) gives: % 88.02/12.51 | (31) all_62_2 = all_53_0 % 88.02/12.51 | % 88.02/12.51 | COMBINE_EQS: (30), (31) imply: % 88.02/12.51 | (32) all_56_0 = all_53_0 % 88.02/12.51 | % 88.02/12.51 | SIMP: (32) implies: % 88.02/12.51 | (33) all_56_0 = all_53_0 % 88.02/12.51 | % 88.02/12.51 | REDUCE: (20), (33) imply: % 88.02/12.51 | (34) $i(all_53_0) % 88.02/12.51 | % 88.02/12.51 | REDUCE: (26), (31) imply: % 88.02/12.51 | (35) aSubsetOf0(all_53_0, all_62_1) % 88.02/12.51 | % 88.02/12.51 | GROUND_INST: instantiating (mEOfElem) with xS, xx, simplifying with (2), (5), % 88.02/12.51 | (8), (13) gives: % 88.02/12.51 | (36) aElement0(xx) % 88.02/12.51 | % 88.02/12.51 | GROUND_INST: instantiating (1) with all_62_1, all_53_0, xP, simplifying with % 88.02/12.51 | (9), (16), (25), (27), (34), (35) gives: % 88.02/12.51 | (37) aElementOf0(xP, all_62_1) % 88.02/12.51 | % 88.02/12.51 | GROUND_INST: instantiating (29) with xP, xk, simplifying with (9), (17) gives: % 88.02/12.51 | (38) ~ aElementOf0(xP, all_62_1) | aSubsetOf0(xP, xT) % 88.02/12.51 | % 88.02/12.51 | BETA: splitting (23) gives: % 88.02/12.51 | % 88.02/12.51 | Case 1: % 88.02/12.51 | | % 88.02/12.51 | | (39) aElementOf0(xx, xP) % 88.02/12.51 | | % 88.02/12.51 | | BETA: splitting (38) gives: % 88.02/12.51 | | % 88.02/12.51 | | Case 1: % 88.02/12.51 | | | % 88.02/12.51 | | | (40) ~ aElementOf0(xP, all_62_1) % 88.02/12.51 | | | % 88.02/12.51 | | | PRED_UNIFY: (37), (40) imply: % 88.02/12.51 | | | (41) $false % 88.02/12.51 | | | % 88.02/12.51 | | | CLOSE: (41) is inconsistent. % 88.02/12.51 | | | % 88.02/12.51 | | Case 2: % 88.02/12.51 | | | % 88.02/12.51 | | | (42) aSubsetOf0(xP, xT) % 88.02/12.51 | | | % 88.02/12.51 | | | GROUND_INST: instantiating (1) with xT, xP, xx, simplifying with (3), (9), % 88.02/12.51 | | | (11), (12), (13), (39), (42) gives: % 88.02/12.51 | | | (43) $false % 88.02/12.51 | | | % 88.02/12.51 | | | CLOSE: (43) is inconsistent. % 88.02/12.51 | | | % 88.02/12.51 | | End of split % 88.02/12.51 | | % 88.02/12.51 | Case 2: % 88.02/12.51 | | % 88.02/12.51 | | (44) ~ aElement0(xx) % 88.02/12.51 | | % 88.02/12.51 | | PRED_UNIFY: (36), (44) imply: % 88.02/12.51 | | (45) $false % 88.02/12.51 | | % 88.02/12.51 | | CLOSE: (45) is inconsistent. % 88.02/12.51 | | % 88.02/12.51 | End of split % 88.02/12.51 | % 88.02/12.51 End of proof % 88.02/12.51 % SZS output end Proof for theBenchmark % 88.02/12.51 % 88.02/12.51 11908ms %------------------------------------------------------------------------------