%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM552+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 : n025.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 11:48:34 EDT 2023 % Result : Theorem 21.35s 3.63s % Output : Proof 28.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM552+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 09:13:06 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/sandbox/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 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 % 3.94/1.27 Prover 1: Preprocessing ... % 3.94/1.27 Prover 4: Preprocessing ... % 3.94/1.31 Prover 5: Preprocessing ... % 3.94/1.31 Prover 6: Preprocessing ... % 3.94/1.32 Prover 0: Preprocessing ... % 3.94/1.32 Prover 2: Preprocessing ... % 3.94/1.32 Prover 3: Preprocessing ... % 11.60/2.35 Prover 5: Proving ... % 11.60/2.35 Prover 2: Proving ... % 11.60/2.35 Prover 3: Constructing countermodel ... % 11.60/2.35 Prover 1: Constructing countermodel ... % 11.60/2.36 Prover 6: Proving ... % 13.85/2.62 Prover 0: Proving ... % 13.85/2.63 Prover 4: Constructing countermodel ... % 21.35/3.63 Prover 0: proved (3009ms) % 21.35/3.63 % 21.35/3.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.35/3.63 % 21.35/3.63 Prover 3: stopped % 21.35/3.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.35/3.64 Prover 5: stopped % 21.35/3.64 Prover 2: stopped % 21.35/3.65 Prover 6: stopped % 21.35/3.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.35/3.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.35/3.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.61/3.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.11/3.87 Prover 7: Preprocessing ... % 23.11/3.90 Prover 13: Preprocessing ... % 23.11/3.91 Prover 8: Preprocessing ... % 23.11/3.92 Prover 11: Preprocessing ... % 23.59/3.94 Prover 10: Preprocessing ... % 24.51/4.06 Prover 7: Constructing countermodel ... % 24.80/4.13 Prover 10: Constructing countermodel ... % 24.80/4.14 Prover 8: Warning: ignoring some quantifiers % 24.80/4.15 Prover 8: Constructing countermodel ... % 24.80/4.16 Prover 13: Constructing countermodel ... % 27.23/4.41 Prover 10: Found proof (size 16) % 27.23/4.41 Prover 10: proved (753ms) % 27.23/4.41 Prover 7: stopped % 27.23/4.41 Prover 13: stopped % 27.23/4.41 Prover 8: stopped % 27.23/4.41 Prover 4: stopped % 27.23/4.41 Prover 1: stopped % 27.78/4.54 Prover 11: Constructing countermodel ... % 27.78/4.56 Prover 11: stopped % 27.78/4.56 % 27.78/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.78/4.56 % 27.78/4.56 % SZS output start Proof for theBenchmark % 27.78/4.57 Assumptions after simplification: % 27.78/4.57 --------------------------------- % 27.78/4.57 % 27.78/4.57 (mDefSub) % 27.78/4.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.78/4.57 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 27.78/4.57 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 27.78/4.57 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 27.78/4.57 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 27.78/4.57 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 27.78/4.57 % 27.78/4.57 (m__) % 27.78/4.57 $i(xQ) & $i(xx) & $i(xT) & aElementOf0(xx, xQ) & ~ aElementOf0(xx, xT) % 27.78/4.57 % 27.78/4.57 (m__2227) % 28.01/4.60 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 28.01/4.60 $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = % 28.01/4.60 v0 & $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & aElementOf0(v2, v0) & % 28.01/4.60 aSet0(v1) & aSet0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 28.01/4.60 (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v3) | ~ % 28.01/4.60 aElementOf0(v3, v1) | aElementOf0(v5, xT)) & ! [v3: $i] : ! [v4: $i] : % 28.01/4.60 ! [v5: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 28.01/4.60 aElementOf0(v5, v3) | ~ aElementOf0(v3, v0) | aElementOf0(v5, xS)) & ! % 28.01/4.60 [v3: $i] : ! [v4: $i] : (v4 = xk | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ % 28.01/4.60 aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : (v4 = xk | ~ % 28.01/4.60 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0)) & ! [v3: $i] : % 28.01/4.60 ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 28.01/4.60 aSubsetOf0(v3, xT)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) % 28.01/4.60 | ~ $i(v3) | ~ aElementOf0(v3, v1) | aSet0(v3)) & ! [v3: $i] : ! [v4: % 28.01/4.60 $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) | % 28.01/4.60 aSubsetOf0(v3, xS)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) % 28.01/4.60 | ~ $i(v3) | ~ aElementOf0(v3, v0) | aSet0(v3)) & ! [v3: $i] : ( ~ % 28.01/4.60 (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSubsetOf0(v3, xT) | aElementOf0(v3, % 28.01/4.60 v1)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ % 28.01/4.60 aSubsetOf0(v3, xS) | aElementOf0(v3, v0)) & ! [v3: $i] : ( ~ % 28.01/4.60 (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | aElementOf0(v3, v1) | ? % 28.01/4.60 [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ aElementOf0(v4, xT))) & ! % 28.01/4.60 [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | % 28.01/4.60 aElementOf0(v3, v0) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ % 28.01/4.60 aElementOf0(v4, xS))) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, % 28.01/4.60 v0) | aElementOf0(v3, v1))) % 28.01/4.60 % 28.01/4.60 (m__2270) % 28.01/4.60 $i(xQ) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & % 28.01/4.60 sbrdtbr0(xQ) = xk & $i(v0) & aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & % 28.01/4.60 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 28.01/4.60 aElementOf0(v1, xS))) % 28.01/4.60 % 28.01/4.60 (function-axioms) % 28.01/4.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.01/4.61 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] % 28.01/4.61 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = % 28.01/4.61 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.01/4.61 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 28.01/4.61 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.01/4.61 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 28.01/4.61 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & % 28.01/4.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) % 28.01/4.61 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 28.01/4.61 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 28.01/4.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 28.01/4.61 (szszuzczcdt0(v2) = v0)) % 28.01/4.61 % 28.01/4.61 Further assumptions not needed in the proof: % 28.01/4.61 -------------------------------------------- % 28.01/4.61 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 28.01/4.61 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 28.01/4.61 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDiffCons, % 28.01/4.61 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, % 28.01/4.61 mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 28.01/4.61 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, % 28.01/4.61 mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, % 28.01/4.61 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, % 28.01/4.61 m__2202, m__2202_02, m__2256, m__2291, m__2304 % 28.01/4.61 % 28.01/4.61 Those formulas are unsatisfiable: % 28.01/4.61 --------------------------------- % 28.01/4.61 % 28.01/4.61 Begin of proof % 28.01/4.61 | % 28.01/4.61 | ALPHA: (mDefSub) implies: % 28.01/4.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 28.01/4.61 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 28.01/4.61 | aSet0(v0) | aElementOf0(v2, v0)) % 28.01/4.61 | % 28.01/4.61 | ALPHA: (m__2227) implies: % 28.01/4.61 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = slcrc0) & % 28.01/4.61 | slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v2) & % 28.01/4.61 | $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & aElementOf0(v2, v0) & % 28.01/4.61 | aSet0(v1) & aSet0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 28.01/4.61 | (sbrdtbr0(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, % 28.01/4.61 | v3) | ~ aElementOf0(v3, v1) | aElementOf0(v5, xT)) & ! [v3: $i] % 28.01/4.61 | : ! [v4: $i] : ! [v5: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v5) | % 28.01/4.61 | ~ $i(v3) | ~ aElementOf0(v5, v3) | ~ aElementOf0(v3, v0) | % 28.01/4.61 | aElementOf0(v5, xS)) & ! [v3: $i] : ! [v4: $i] : (v4 = xk | ~ % 28.01/4.61 | (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & ! [v3: % 28.01/4.61 | $i] : ! [v4: $i] : (v4 = xk | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | % 28.01/4.61 | ~ aElementOf0(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 28.01/4.61 | (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 28.01/4.61 | aSubsetOf0(v3, xT)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) % 28.01/4.61 | = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | aSet0(v3)) & ! [v3: % 28.01/4.61 | $i] : ! [v4: $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ % 28.01/4.61 | aElementOf0(v3, v0) | aSubsetOf0(v3, xS)) & ! [v3: $i] : ! [v4: % 28.01/4.61 | $i] : ( ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) % 28.01/4.61 | | aSet0(v3)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | % 28.01/4.61 | ~ aSubsetOf0(v3, xT) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ % 28.01/4.61 | (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSubsetOf0(v3, xS) | % 28.01/4.61 | aElementOf0(v3, v0)) & ! [v3: $i] : ( ~ (sbrdtbr0(v3) = xk) | ~ % 28.01/4.61 | $i(v3) | ~ aSet0(v3) | aElementOf0(v3, v1) | ? [v4: $i] : ($i(v4) % 28.01/4.61 | & aElementOf0(v4, v3) & ~ aElementOf0(v4, xT))) & ! [v3: $i] : % 28.01/4.61 | ( ~ (sbrdtbr0(v3) = xk) | ~ $i(v3) | ~ aSet0(v3) | aElementOf0(v3, % 28.01/4.61 | v0) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v3) & ~ % 28.01/4.61 | aElementOf0(v4, xS))) & ! [v3: $i] : ( ~ $i(v3) | ~ % 28.01/4.61 | aElementOf0(v3, v0) | aElementOf0(v3, v1))) % 28.01/4.61 | % 28.01/4.61 | ALPHA: (m__2270) implies: % 28.01/4.62 | (3) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & sbrdtbr0(xQ) = xk & $i(v0) & % 28.01/4.62 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 28.01/4.62 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xS))) % 28.01/4.62 | % 28.01/4.62 | ALPHA: (m__) implies: % 28.01/4.62 | (4) ~ aElementOf0(xx, xT) % 28.01/4.62 | (5) aElementOf0(xx, xQ) % 28.01/4.62 | (6) $i(xx) % 28.01/4.62 | (7) $i(xQ) % 28.01/4.62 | % 28.01/4.62 | ALPHA: (function-axioms) implies: % 28.01/4.62 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.01/4.62 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) % 28.01/4.62 | % 28.01/4.62 | DELTA: instantiating (3) with fresh symbol all_53_0 gives: % 28.01/4.62 | (9) slbdtsldtrb0(xS, xk) = all_53_0 & sbrdtbr0(xQ) = xk & $i(all_53_0) & % 28.01/4.62 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, all_53_0) & aSet0(xQ) & ! [v0: % 28.01/4.62 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xS)) % 28.01/4.62 | % 28.01/4.62 | ALPHA: (9) implies: % 28.01/4.62 | (10) aElementOf0(xQ, all_53_0) % 28.01/4.62 | (11) sbrdtbr0(xQ) = xk % 28.01/4.62 | (12) slbdtsldtrb0(xS, xk) = all_53_0 % 28.01/4.62 | % 28.01/4.62 | DELTA: instantiating (2) with fresh symbols all_56_0, all_56_1, all_56_2 % 28.01/4.62 | gives: % 28.01/4.62 | (13) ~ (all_56_2 = slcrc0) & slbdtsldtrb0(xT, xk) = all_56_1 & % 28.01/4.62 | slbdtsldtrb0(xS, xk) = all_56_2 & $i(all_56_0) & $i(all_56_1) & % 28.01/4.62 | $i(all_56_2) & aSubsetOf0(all_56_2, all_56_1) & aElementOf0(all_56_0, % 28.01/4.62 | all_56_2) & aSet0(all_56_1) & aSet0(all_56_2) & ! [v0: $i] : ! % 28.01/4.62 | [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ % 28.01/4.62 | $i(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v0, all_56_1) | % 28.01/4.62 | aElementOf0(v2, xT)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 28.01/4.62 | (sbrdtbr0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v0) % 28.01/4.62 | | ~ aElementOf0(v0, all_56_2) | aElementOf0(v2, xS)) & ! [v0: $i] % 28.01/4.62 | : ! [v1: $i] : (v1 = xk | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 28.01/4.62 | aElementOf0(v0, all_56_1)) & ! [v0: $i] : ! [v1: $i] : (v1 = xk | % 28.01/4.62 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_56_2)) & % 28.01/4.62 | ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 28.01/4.62 | aElementOf0(v0, all_56_1) | aSubsetOf0(v0, xT)) & ! [v0: $i] : ! % 28.01/4.62 | [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 28.01/4.63 | all_56_1) | aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 28.01/4.63 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_56_2) | % 28.01/4.63 | aSubsetOf0(v0, xS)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) % 28.01/4.63 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_56_2) | aSet0(v0)) & ! % 28.01/4.63 | [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSubsetOf0(v0, xT) % 28.01/4.63 | | aElementOf0(v0, all_56_1)) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) % 28.01/4.63 | | ~ $i(v0) | ~ aSubsetOf0(v0, xS) | aElementOf0(v0, all_56_2)) & % 28.01/4.63 | ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSet0(v0) | % 28.01/4.63 | aElementOf0(v0, all_56_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, % 28.01/4.63 | v0) & ~ aElementOf0(v1, xT))) & ! [v0: $i] : ( ~ (sbrdtbr0(v0) % 28.01/4.63 | = xk) | ~ $i(v0) | ~ aSet0(v0) | aElementOf0(v0, all_56_2) | ? % 28.01/4.63 | [v1: $i] : ($i(v1) & aElementOf0(v1, v0) & ~ aElementOf0(v1, xS))) % 28.01/4.63 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_56_2) | % 28.01/4.63 | aElementOf0(v0, all_56_1)) % 28.01/4.63 | % 28.01/4.63 | ALPHA: (13) implies: % 28.01/4.63 | (14) aSet0(all_56_1) % 28.01/4.63 | (15) aSubsetOf0(all_56_2, all_56_1) % 28.01/4.63 | (16) $i(all_56_2) % 28.01/4.63 | (17) $i(all_56_1) % 28.01/4.63 | (18) slbdtsldtrb0(xS, xk) = all_56_2 % 28.01/4.63 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ % 28.01/4.63 | $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v0, % 28.01/4.63 | all_56_1) | aElementOf0(v2, xT)) % 28.01/4.63 | % 28.01/4.63 | GROUND_INST: instantiating (8) with all_53_0, all_56_2, xk, xS, simplifying % 28.01/4.63 | with (12), (18) gives: % 28.01/4.63 | (20) all_56_2 = all_53_0 % 28.01/4.63 | % 28.01/4.63 | REDUCE: (16), (20) imply: % 28.01/4.63 | (21) $i(all_53_0) % 28.01/4.63 | % 28.01/4.63 | REDUCE: (15), (20) imply: % 28.01/4.63 | (22) aSubsetOf0(all_53_0, all_56_1) % 28.01/4.63 | % 28.01/4.63 | GROUND_INST: instantiating (1) with all_56_1, all_53_0, xQ, simplifying with % 28.01/4.63 | (7), (10), (14), (17), (21), (22) gives: % 28.01/4.63 | (23) aElementOf0(xQ, all_56_1) % 28.01/4.63 | % 28.01/4.63 | GROUND_INST: instantiating (19) with xQ, xk, xx, simplifying with (4), (5), % 28.01/4.63 | (6), (7), (11), (23) gives: % 28.01/4.63 | (24) $false % 28.01/4.63 | % 28.01/4.63 | CLOSE: (24) is inconsistent. % 28.01/4.63 | % 28.01/4.63 End of proof % 28.01/4.63 % SZS output end Proof for theBenchmark % 28.01/4.63 % 28.01/4.63 4029ms %------------------------------------------------------------------------------