%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM535+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 11:48:27 EDT 2023 % Result : Theorem 19.06s 3.33s % Output : Proof 19.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM535+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n020.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Fri Aug 25 15:40:15 EDT 2023 % 0.17/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.19/1.04 Prover 1: Preprocessing ... % 2.19/1.04 Prover 4: Preprocessing ... % 2.92/1.08 Prover 6: Preprocessing ... % 2.92/1.08 Prover 0: Preprocessing ... % 2.92/1.08 Prover 3: Preprocessing ... % 2.92/1.08 Prover 2: Preprocessing ... % 2.92/1.08 Prover 5: Preprocessing ... % 4.94/1.51 Prover 1: Constructing countermodel ... % 5.94/1.52 Prover 5: Constructing countermodel ... % 5.94/1.54 Prover 3: Constructing countermodel ... % 5.94/1.55 Prover 2: Proving ... % 6.39/1.60 Prover 6: Proving ... % 7.49/1.77 Prover 4: Constructing countermodel ... % 8.58/1.89 Prover 0: Proving ... % 9.10/2.09 Prover 1: gave up % 9.10/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.56/2.17 Prover 7: Preprocessing ... % 11.63/2.30 Prover 7: Constructing countermodel ... % 12.32/2.38 Prover 3: gave up % 12.32/2.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.63/2.46 Prover 8: Preprocessing ... % 13.27/2.55 Prover 8: Warning: ignoring some quantifiers % 13.27/2.55 Prover 8: Constructing countermodel ... % 15.77/2.94 Prover 8: gave up % 16.46/2.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 16.79/3.00 Prover 9: Preprocessing ... % 18.08/3.20 Prover 9: Constructing countermodel ... % 19.06/3.32 Prover 7: Found proof (size 61) % 19.06/3.32 Prover 7: proved (1211ms) % 19.06/3.32 Prover 5: stopped % 19.06/3.32 Prover 2: stopped % 19.06/3.32 Prover 4: stopped % 19.06/3.32 Prover 0: stopped % 19.06/3.32 Prover 6: stopped % 19.06/3.33 Prover 9: stopped % 19.06/3.33 % 19.06/3.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.06/3.33 % 19.06/3.34 % SZS output start Proof for theBenchmark % 19.06/3.34 Assumptions after simplification: % 19.06/3.34 --------------------------------- % 19.06/3.34 % 19.06/3.34 (mDefCons) % 19.37/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 19.37/3.37 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 19.37/3.37 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 19.37/3.37 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 19.37/3.37 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = % 19.37/3.37 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.37/3.37 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ % 19.37/3.37 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | % 19.37/3.37 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.37/3.37 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 19.37/3.37 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 19.37/3.37 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.37/3.37 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 19.37/3.37 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ % 19.37/3.37 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.37/3.37 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.37/3.37 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1: % 19.37/3.37 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ % 19.37/3.37 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 19.37/3.37 % 19.37/3.37 (mDefDiff) % 19.37/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 19.37/3.38 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 19.37/3.38 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 19.37/3.38 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 19.37/3.38 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 19.37/3.38 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 19.37/3.38 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 19.37/3.38 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 19.37/3.38 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 19.37/3.38 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 19.37/3.38 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 19.37/3.38 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.37/3.38 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 19.37/3.38 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 19.37/3.38 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 19.37/3.38 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.37/3.38 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 19.37/3.38 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 19.37/3.38 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 19.37/3.38 % 19.37/3.38 (mDefSub) % 19.37/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.37/3.38 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 19.37/3.38 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 19.37/3.38 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 19.37/3.38 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 19.37/3.38 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 19.37/3.38 % 19.37/3.38 (mEOfElem) % 19.37/3.38 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 19.37/3.38 ~ aSet0(v0) | aElement0(v1)) % 19.37/3.38 % 19.37/3.38 (m__) % 19.37/3.38 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : (sdtmndt0(xS, xx) = v0 & % 19.37/3.38 sdtpldt0(v0, xx) = v1 & $i(v1) & $i(v0) & ( ~ aSubsetOf0(v1, xS) | ~ % 19.37/3.38 aSubsetOf0(xS, v1))) % 19.37/3.38 % 19.37/3.38 (m__617) % 19.37/3.38 $i(xS) & aSet0(xS) % 19.37/3.38 % 19.37/3.38 (m__617_02) % 19.37/3.38 $i(xx) & $i(xS) & aElementOf0(xx, xS) % 19.37/3.38 % 19.37/3.38 Further assumptions not needed in the proof: % 19.37/3.38 -------------------------------------------- % 19.37/3.38 mCntRel, mCountNFin, mCountNFin_01, mDefEmp, mElmSort, mEmpFin, mFinRel, % 19.37/3.38 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans % 19.37/3.38 % 19.37/3.38 Those formulas are unsatisfiable: % 19.37/3.38 --------------------------------- % 19.37/3.38 % 19.37/3.38 Begin of proof % 19.37/3.38 | % 19.37/3.39 | ALPHA: (mDefSub) implies: % 19.37/3.39 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 19.37/3.39 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 19.37/3.39 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 19.37/3.39 | % 19.37/3.39 | ALPHA: (mDefCons) implies: % 19.37/3.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 19.37/3.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 19.37/3.39 | aSet0(v2)) % 19.37/3.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 19.37/3.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 19.37/3.39 | aElementOf0(v1, v2)) % 19.37/3.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 19.37/3.39 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.37/3.39 | $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) % 19.37/3.39 | | ~ aSet0(v0) | aElementOf0(v3, v2)) % 19.37/3.39 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 19.37/3.39 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.37/3.39 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 19.37/3.39 | aElementOf0(v3, v0)) % 19.37/3.39 | % 19.37/3.39 | ALPHA: (mDefDiff) implies: % 19.37/3.39 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | % 19.37/3.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 19.37/3.39 | aSet0(v2)) % 19.37/3.39 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | % 19.37/3.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~ % 19.37/3.39 | aElement0(v1) | ~ aSet0(v0)) % 19.37/3.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 19.37/3.39 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.37/3.39 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 19.37/3.39 | aElementOf0(v3, v0)) % 19.37/3.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 19.37/3.39 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.37/3.39 | $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) % 19.37/3.39 | | ~ aSet0(v0) | aElementOf0(v3, v2)) % 19.37/3.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 19.37/3.39 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 19.37/3.40 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) % 19.37/3.40 | & (v4 = v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ % 19.37/3.40 | aElement0(v4)) & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & % 19.37/3.40 | aElementOf0(v4, v0) & aElement0(v4))))) % 19.37/3.40 | % 19.37/3.40 | ALPHA: (m__617) implies: % 19.37/3.40 | (11) aSet0(xS) % 19.37/3.40 | % 19.37/3.40 | ALPHA: (m__617_02) implies: % 19.37/3.40 | (12) aElementOf0(xx, xS) % 19.37/3.40 | % 19.37/3.40 | ALPHA: (m__) implies: % 19.37/3.40 | (13) $i(xS) % 19.37/3.40 | (14) $i(xx) % 19.37/3.40 | (15) ? [v0: $i] : ? [v1: $i] : (sdtmndt0(xS, xx) = v0 & sdtpldt0(v0, xx) % 19.37/3.40 | = v1 & $i(v1) & $i(v0) & ( ~ aSubsetOf0(v1, xS) | ~ aSubsetOf0(xS, % 19.37/3.40 | v1))) % 19.37/3.40 | % 19.37/3.40 | DELTA: instantiating (15) with fresh symbols all_14_0, all_14_1 gives: % 19.37/3.40 | (16) sdtmndt0(xS, xx) = all_14_1 & sdtpldt0(all_14_1, xx) = all_14_0 & % 19.37/3.40 | $i(all_14_0) & $i(all_14_1) & ( ~ aSubsetOf0(all_14_0, xS) | ~ % 19.37/3.40 | aSubsetOf0(xS, all_14_0)) % 19.37/3.40 | % 19.37/3.40 | ALPHA: (16) implies: % 19.37/3.40 | (17) $i(all_14_1) % 19.37/3.40 | (18) $i(all_14_0) % 19.37/3.40 | (19) sdtpldt0(all_14_1, xx) = all_14_0 % 19.37/3.40 | (20) sdtmndt0(xS, xx) = all_14_1 % 19.37/3.40 | (21) ~ aSubsetOf0(all_14_0, xS) | ~ aSubsetOf0(xS, all_14_0) % 19.37/3.40 | % 19.37/3.40 | GROUND_INST: instantiating (mEOfElem) with xS, xx, simplifying with (11), % 19.37/3.40 | (12), (13), (14) gives: % 19.37/3.40 | (22) aElement0(xx) % 19.37/3.40 | % 19.37/3.40 | GROUND_INST: instantiating (10) with xS, xx, all_14_1, xS, simplifying with % 19.37/3.40 | (11), (13), (14), (20), (22) gives: % 19.37/3.40 | (23) all_14_1 = xS | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & (v0 = xx % 19.37/3.40 | | ~ aElement0(v0))) % 19.37/3.40 | % 19.37/3.40 | GROUND_INST: instantiating (6) with xS, xx, all_14_1, simplifying with (11), % 19.37/3.40 | (13), (14), (17), (20), (22) gives: % 19.37/3.40 | (24) aSet0(all_14_1) % 19.37/3.40 | % 19.37/3.40 | GROUND_INST: instantiating (7) with xS, xx, xS, simplifying with (11), (12), % 19.37/3.40 | (13), (14), (22) gives: % 19.37/3.40 | (25) ~ (sdtmndt0(xS, xx) = xS) % 19.37/3.40 | % 19.37/3.40 | PRED_UNIFY: (20), (25) imply: % 19.37/3.40 | (26) ~ (all_14_1 = xS) % 19.37/3.40 | % 19.37/3.40 | BETA: splitting (23) gives: % 19.37/3.40 | % 19.37/3.40 | Case 1: % 19.37/3.40 | | % 19.37/3.40 | | (27) all_14_1 = xS % 19.37/3.40 | | % 19.37/3.40 | | REDUCE: (26), (27) imply: % 19.37/3.40 | | (28) $false % 19.37/3.40 | | % 19.37/3.40 | | CLOSE: (28) is inconsistent. % 19.37/3.40 | | % 19.37/3.40 | Case 2: % 19.37/3.40 | | % 19.37/3.40 | | (29) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & (v0 = xx | ~ % 19.37/3.40 | | aElement0(v0))) % 19.37/3.40 | | % 19.37/3.40 | | DELTA: instantiating (29) with fresh symbol all_50_0 gives: % 19.37/3.40 | | (30) $i(all_50_0) & aElementOf0(all_50_0, xS) & (all_50_0 = xx | ~ % 19.37/3.40 | | aElement0(all_50_0)) % 19.37/3.40 | | % 19.37/3.40 | | ALPHA: (30) implies: % 19.37/3.41 | | (31) aElementOf0(all_50_0, xS) % 19.37/3.41 | | (32) $i(all_50_0) % 19.37/3.41 | | (33) all_50_0 = xx | ~ aElement0(all_50_0) % 19.37/3.41 | | % 19.37/3.41 | | GROUND_INST: instantiating (3) with all_14_1, xx, all_14_0, simplifying with % 19.37/3.41 | | (14), (17), (18), (19), (22), (24) gives: % 19.37/3.41 | | (34) aElementOf0(xx, all_14_0) % 19.37/3.41 | | % 19.37/3.41 | | GROUND_INST: instantiating (2) with all_14_1, xx, all_14_0, simplifying with % 19.37/3.41 | | (14), (17), (18), (19), (22), (24) gives: % 19.37/3.41 | | (35) aSet0(all_14_0) % 19.37/3.41 | | % 19.37/3.41 | | GROUND_INST: instantiating (mEOfElem) with xS, all_50_0, simplifying with % 19.37/3.41 | | (11), (13), (31), (32) gives: % 19.37/3.41 | | (36) aElement0(all_50_0) % 19.37/3.41 | | % 19.37/3.41 | | BETA: splitting (33) gives: % 19.37/3.41 | | % 19.37/3.41 | | Case 1: % 19.37/3.41 | | | % 19.37/3.41 | | | (37) ~ aElement0(all_50_0) % 19.37/3.41 | | | % 19.37/3.41 | | | PRED_UNIFY: (36), (37) imply: % 19.37/3.41 | | | (38) $false % 19.37/3.41 | | | % 19.37/3.41 | | | CLOSE: (38) is inconsistent. % 19.37/3.41 | | | % 19.37/3.41 | | Case 2: % 19.37/3.41 | | | % 19.37/3.41 | | | (39) all_50_0 = xx % 19.37/3.41 | | | % 19.37/3.41 | | | GROUND_INST: instantiating (1) with xS, all_14_0, simplifying with (11), % 19.37/3.41 | | | (13), (18), (35) gives: % 19.37/3.41 | | | (40) aSubsetOf0(all_14_0, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 19.37/3.41 | | | all_14_0) & ~ aElementOf0(v0, xS)) % 19.37/3.41 | | | % 19.37/3.41 | | | GROUND_INST: instantiating (1) with all_14_0, xS, simplifying with (11), % 19.37/3.41 | | | (13), (18), (35) gives: % 19.37/3.41 | | | (41) aSubsetOf0(xS, all_14_0) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 19.37/3.41 | | | xS) & ~ aElementOf0(v0, all_14_0)) % 19.37/3.41 | | | % 19.37/3.41 | | | BETA: splitting (21) gives: % 19.37/3.41 | | | % 19.37/3.41 | | | Case 1: % 19.37/3.41 | | | | % 19.37/3.41 | | | | (42) ~ aSubsetOf0(all_14_0, xS) % 19.37/3.41 | | | | % 19.37/3.41 | | | | BETA: splitting (40) gives: % 19.37/3.41 | | | | % 19.37/3.41 | | | | Case 1: % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | (43) aSubsetOf0(all_14_0, xS) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | PRED_UNIFY: (42), (43) imply: % 19.37/3.41 | | | | | (44) $false % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | CLOSE: (44) is inconsistent. % 19.37/3.41 | | | | | % 19.37/3.41 | | | | Case 2: % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | (45) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_14_0) & ~ % 19.37/3.41 | | | | | aElementOf0(v0, xS)) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | DELTA: instantiating (45) with fresh symbol all_120_0 gives: % 19.37/3.41 | | | | | (46) $i(all_120_0) & aElementOf0(all_120_0, all_14_0) & ~ % 19.37/3.41 | | | | | aElementOf0(all_120_0, xS) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | ALPHA: (46) implies: % 19.37/3.41 | | | | | (47) ~ aElementOf0(all_120_0, xS) % 19.37/3.41 | | | | | (48) aElementOf0(all_120_0, all_14_0) % 19.37/3.41 | | | | | (49) $i(all_120_0) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | PRED_UNIFY: (12), (47) imply: % 19.37/3.41 | | | | | (50) ~ (all_120_0 = xx) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | GROUND_INST: instantiating (5) with all_14_1, xx, all_14_0, all_120_0, % 19.37/3.41 | | | | | simplifying with (14), (17), (18), (19), (22), (24), % 19.37/3.41 | | | | | (48), (49) gives: % 19.37/3.41 | | | | | (51) all_120_0 = xx | aElementOf0(all_120_0, all_14_1) % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | BETA: splitting (51) gives: % 19.37/3.41 | | | | | % 19.37/3.41 | | | | | Case 1: % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | (52) aElementOf0(all_120_0, all_14_1) % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | GROUND_INST: instantiating (8) with xS, xx, all_14_1, all_120_0, % 19.37/3.41 | | | | | | simplifying with (11), (13), (14), (17), (20), (22), % 19.37/3.41 | | | | | | (47), (49), (52) gives: % 19.37/3.41 | | | | | | (53) $false % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | CLOSE: (53) is inconsistent. % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | Case 2: % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | (54) all_120_0 = xx % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | REDUCE: (50), (54) imply: % 19.37/3.41 | | | | | | (55) $false % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | | CLOSE: (55) is inconsistent. % 19.37/3.41 | | | | | | % 19.37/3.41 | | | | | End of split % 19.37/3.41 | | | | | % 19.37/3.41 | | | | End of split % 19.37/3.41 | | | | % 19.37/3.41 | | | Case 2: % 19.37/3.41 | | | | % 19.37/3.41 | | | | (56) ~ aSubsetOf0(xS, all_14_0) % 19.37/3.42 | | | | % 19.37/3.42 | | | | BETA: splitting (41) gives: % 19.37/3.42 | | | | % 19.37/3.42 | | | | Case 1: % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | (57) aSubsetOf0(xS, all_14_0) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | PRED_UNIFY: (56), (57) imply: % 19.37/3.42 | | | | | (58) $false % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | CLOSE: (58) is inconsistent. % 19.37/3.42 | | | | | % 19.37/3.42 | | | | Case 2: % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | (59) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & ~ % 19.37/3.42 | | | | | aElementOf0(v0, all_14_0)) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | DELTA: instantiating (59) with fresh symbol all_120_0 gives: % 19.37/3.42 | | | | | (60) $i(all_120_0) & aElementOf0(all_120_0, xS) & ~ % 19.37/3.42 | | | | | aElementOf0(all_120_0, all_14_0) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | ALPHA: (60) implies: % 19.37/3.42 | | | | | (61) ~ aElementOf0(all_120_0, all_14_0) % 19.37/3.42 | | | | | (62) aElementOf0(all_120_0, xS) % 19.37/3.42 | | | | | (63) $i(all_120_0) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | PRED_UNIFY: (34), (61) imply: % 19.37/3.42 | | | | | (64) ~ (all_120_0 = xx) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_120_0, simplifying % 19.37/3.42 | | | | | with (11), (13), (62), (63) gives: % 19.37/3.42 | | | | | (65) aElement0(all_120_0) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | GROUND_INST: instantiating (9) with xS, xx, all_14_1, all_120_0, % 19.37/3.42 | | | | | simplifying with (11), (13), (14), (17), (20), (22), % 19.37/3.42 | | | | | (62), (63), (65) gives: % 19.37/3.42 | | | | | (66) all_120_0 = xx | aElementOf0(all_120_0, all_14_1) % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | BETA: splitting (66) gives: % 19.37/3.42 | | | | | % 19.37/3.42 | | | | | Case 1: % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | (67) aElementOf0(all_120_0, all_14_1) % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | GROUND_INST: instantiating (4) with all_14_1, xx, all_14_0, % 19.37/3.42 | | | | | | all_120_0, simplifying with (14), (17), (18), (19), % 19.37/3.42 | | | | | | (22), (24), (61), (63), (65), (67) gives: % 19.37/3.42 | | | | | | (68) $false % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | CLOSE: (68) is inconsistent. % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | Case 2: % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | (69) all_120_0 = xx % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | REDUCE: (64), (69) imply: % 19.37/3.42 | | | | | | (70) $false % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | | CLOSE: (70) is inconsistent. % 19.37/3.42 | | | | | | % 19.37/3.42 | | | | | End of split % 19.37/3.42 | | | | | % 19.37/3.42 | | | | End of split % 19.37/3.42 | | | | % 19.37/3.42 | | | End of split % 19.37/3.42 | | | % 19.37/3.42 | | End of split % 19.37/3.42 | | % 19.37/3.42 | End of split % 19.37/3.42 | % 19.37/3.42 End of proof % 19.37/3.42 % SZS output end Proof for theBenchmark % 19.37/3.42 % 19.37/3.42 2807ms %------------------------------------------------------------------------------