%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM537+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 11:48:28 EDT 2023 % Result : Theorem 35.44s 5.57s % Output : Proof 35.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM537+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n020.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 10:44:00 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.37/1.12 Prover 1: Preprocessing ... % 2.37/1.12 Prover 4: Preprocessing ... % 2.85/1.15 Prover 2: Preprocessing ... % 2.85/1.15 Prover 0: Preprocessing ... % 2.85/1.15 Prover 5: Preprocessing ... % 2.85/1.15 Prover 3: Preprocessing ... % 2.85/1.15 Prover 6: Preprocessing ... % 5.89/1.60 Prover 5: Constructing countermodel ... % 5.89/1.61 Prover 1: Constructing countermodel ... % 5.89/1.61 Prover 6: Proving ... % 5.89/1.62 Prover 2: Proving ... % 5.89/1.64 Prover 3: Constructing countermodel ... % 7.14/1.78 Prover 4: Constructing countermodel ... % 8.13/1.87 Prover 0: Proving ... % 11.38/2.34 Prover 3: gave up % 11.38/2.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.64/2.40 Prover 7: Preprocessing ... % 12.39/2.47 Prover 7: Constructing countermodel ... % 13.12/2.61 Prover 1: gave up % 13.12/2.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.12/2.63 Prover 8: Preprocessing ... % 13.65/2.78 Prover 8: Warning: ignoring some quantifiers % 13.65/2.78 Prover 8: Constructing countermodel ... % 17.55/3.17 Prover 8: gave up % 17.55/3.19 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 17.82/3.21 Prover 9: Preprocessing ... % 18.13/3.37 Prover 9: Constructing countermodel ... % 35.44/5.55 Prover 7: Found proof (size 63) % 35.44/5.55 Prover 7: proved (3203ms) % 35.44/5.55 Prover 5: stopped % 35.44/5.55 Prover 2: stopped % 35.44/5.55 Prover 6: stopped % 35.44/5.55 Prover 4: stopped % 35.44/5.56 Prover 9: stopped % 35.44/5.56 Prover 0: stopped % 35.44/5.56 % 35.44/5.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 35.44/5.57 % 35.44/5.57 % SZS output start Proof for theBenchmark % 35.44/5.57 Assumptions after simplification: % 35.44/5.57 --------------------------------- % 35.44/5.57 % 35.44/5.57 (mConsDiff) % 35.44/5.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ % 35.44/5.60 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | ~ aSet0(v0) | sdtpldt0(v2, % 35.44/5.60 v1) = v0) % 35.44/5.60 % 35.44/5.60 (mCountNFin_01) % 35.44/5.60 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 35.44/5.60 % 35.44/5.60 (mDefCons) % 35.44/5.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 35.44/5.61 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.61 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 35.44/5.61 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 35.44/5.61 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = % 35.44/5.61 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 35.44/5.61 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ % 35.44/5.61 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | % 35.44/5.61 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 35.44/5.61 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 35.44/5.61 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 35.44/5.61 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 35.44/5.61 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 35.44/5.61 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ % 35.44/5.61 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 35.44/5.61 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.61 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1: % 35.44/5.61 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ % 35.44/5.61 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 35.44/5.61 % 35.44/5.61 (mDefDiff) % 35.44/5.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 35.44/5.61 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.61 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 35.44/5.61 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 35.44/5.61 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 35.44/5.61 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 35.44/5.61 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 35.44/5.61 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 35.44/5.61 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 35.44/5.61 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 35.44/5.61 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 35.44/5.61 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 35.44/5.61 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 35.44/5.61 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 35.44/5.61 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 35.44/5.61 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.61 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 35.44/5.61 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 35.44/5.61 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 35.44/5.61 % 35.44/5.61 (mDefEmp) % 35.44/5.61 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 35.44/5.61 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 35.44/5.61 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 35.44/5.61 % 35.44/5.61 (mDefSub) % 35.44/5.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 35.44/5.61 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 35.44/5.61 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 35.44/5.61 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 35.44/5.61 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 35.44/5.61 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 35.44/5.61 % 35.44/5.61 (mEOfElem) % 35.44/5.61 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 35.44/5.61 ~ aSet0(v0) | aElement0(v1)) % 35.44/5.61 % 35.44/5.61 (m__) % 35.44/5.61 $i(xS) & $i(xx) & ? [v0: $i] : ? [v1: $i] : (sdtmndt0(v0, xx) = v1 & % 35.44/5.61 sdtpldt0(xS, xx) = v0 & $i(v1) & $i(v0) & ( ~ aSubsetOf0(v1, xS) | ~ % 35.44/5.61 aSubsetOf0(xS, v1))) % 35.44/5.61 % 35.44/5.61 (m__679) % 35.44/5.61 $i(xS) & $i(xx) & aElement0(xx) & aSet0(xS) % 35.44/5.61 % 35.44/5.61 (m__679_02) % 35.44/5.61 $i(xS) & $i(xx) & ~ aElementOf0(xx, xS) % 35.44/5.61 % 35.44/5.61 Further assumptions not needed in the proof: % 35.44/5.61 -------------------------------------------- % 35.44/5.62 mCntRel, mCountNFin, mElmSort, mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, % 35.44/5.62 mSubRefl, mSubTrans % 35.44/5.62 % 35.44/5.62 Those formulas are unsatisfiable: % 35.44/5.62 --------------------------------- % 35.44/5.62 % 35.44/5.62 Begin of proof % 35.44/5.62 | % 35.44/5.62 | ALPHA: (mDefEmp) implies: % 35.44/5.62 | (1) aSet0(slcrc0) % 35.44/5.62 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (mCountNFin_01) implies: % 35.44/5.62 | (3) $i(slcrc0) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (mDefSub) implies: % 35.44/5.62 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 35.44/5.62 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 35.44/5.62 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (mDefCons) implies: % 35.44/5.62 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 35.44/5.62 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 35.44/5.62 | aSet0(v2)) % 35.44/5.62 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 35.44/5.62 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 35.44/5.62 | aElementOf0(v1, v2)) % 35.44/5.62 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 35.44/5.62 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 35.44/5.62 | $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) % 35.44/5.62 | | ~ aSet0(v0) | aElementOf0(v3, v2)) % 35.44/5.62 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 35.44/5.62 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 35.44/5.62 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 35.44/5.62 | aElementOf0(v3, v0)) % 35.44/5.62 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 35.44/5.62 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.62 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & % 35.44/5.62 | ( ~ aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 35.44/5.62 | aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & % 35.44/5.62 | (v4 = v1 | aElementOf0(v4, v0)))))) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (mDefDiff) implies: % 35.44/5.62 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) % 35.44/5.62 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 35.44/5.62 | aSet0(v0) | aSet0(v2)) % 35.44/5.62 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) % 35.44/5.62 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~ % 35.44/5.62 | aElement0(v1) | ~ aSet0(v0)) % 35.44/5.62 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 35.44/5.62 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 35.44/5.62 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 35.44/5.62 | aElementOf0(v3, v0)) % 35.44/5.62 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 35.44/5.62 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 35.44/5.62 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) % 35.44/5.62 | & (v4 = v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ % 35.44/5.62 | aElement0(v4)) & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & % 35.44/5.62 | aElementOf0(v4, v0) & aElement0(v4))))) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (m__679) implies: % 35.44/5.62 | (14) aSet0(xS) % 35.44/5.62 | (15) aElement0(xx) % 35.44/5.62 | % 35.44/5.62 | ALPHA: (m__679_02) implies: % 35.44/5.63 | (16) ~ aElementOf0(xx, xS) % 35.44/5.63 | % 35.44/5.63 | ALPHA: (m__) implies: % 35.44/5.63 | (17) $i(xx) % 35.44/5.63 | (18) $i(xS) % 35.44/5.63 | (19) ? [v0: $i] : ? [v1: $i] : (sdtmndt0(v0, xx) = v1 & sdtpldt0(xS, xx) % 35.44/5.63 | = v0 & $i(v1) & $i(v0) & ( ~ aSubsetOf0(v1, xS) | ~ aSubsetOf0(xS, % 35.44/5.63 | v1))) % 35.44/5.63 | % 35.44/5.63 | DELTA: instantiating (19) with fresh symbols all_15_0, all_15_1 gives: % 35.44/5.63 | (20) sdtmndt0(all_15_1, xx) = all_15_0 & sdtpldt0(xS, xx) = all_15_1 & % 35.44/5.63 | $i(all_15_0) & $i(all_15_1) & ( ~ aSubsetOf0(all_15_0, xS) | ~ % 35.44/5.63 | aSubsetOf0(xS, all_15_0)) % 35.44/5.63 | % 35.44/5.63 | ALPHA: (20) implies: % 35.44/5.63 | (21) $i(all_15_1) % 35.44/5.63 | (22) $i(all_15_0) % 35.44/5.63 | (23) sdtpldt0(xS, xx) = all_15_1 % 35.44/5.63 | (24) sdtmndt0(all_15_1, xx) = all_15_0 % 35.44/5.63 | (25) ~ aSubsetOf0(all_15_0, xS) | ~ aSubsetOf0(xS, all_15_0) % 35.44/5.63 | % 35.44/5.63 | GROUND_INST: instantiating (4) with xS, slcrc0, simplifying with (1), (3), % 35.44/5.63 | (14), (18) gives: % 35.44/5.63 | (26) aSubsetOf0(slcrc0, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 35.44/5.63 | slcrc0) & ~ aElementOf0(v0, xS)) % 35.44/5.63 | % 35.44/5.63 | GROUND_INST: instantiating (9) with xS, xx, all_15_1, xS, simplifying with % 35.44/5.63 | (14), (15), (17), (18), (23) gives: % 35.44/5.63 | (27) all_15_1 = xS | ? [v0: $i] : ($i(v0) & (v0 = xx | aElementOf0(v0, % 35.44/5.63 | xS)) & ( ~ aElementOf0(v0, xS) | ~ aElement0(v0))) % 35.44/5.63 | % 35.44/5.63 | GROUND_INST: instantiating (6) with xS, xx, all_15_1, simplifying with (14), % 35.44/5.63 | (15), (17), (18), (21), (23) gives: % 35.44/5.63 | (28) aElementOf0(xx, all_15_1) % 35.44/5.63 | % 35.44/5.63 | GROUND_INST: instantiating (5) with xS, xx, all_15_1, simplifying with (14), % 35.44/5.63 | (15), (17), (18), (21), (23) gives: % 35.44/5.63 | (29) aSet0(all_15_1) % 35.44/5.63 | % 35.44/5.63 | PRED_UNIFY: (16), (28) imply: % 35.44/5.63 | (30) ~ (all_15_1 = xS) % 35.44/5.63 | % 35.44/5.63 | BETA: splitting (27) gives: % 35.44/5.63 | % 35.44/5.63 | Case 1: % 35.44/5.63 | | % 35.44/5.63 | | (31) all_15_1 = xS % 35.44/5.63 | | % 35.44/5.63 | | REDUCE: (30), (31) imply: % 35.44/5.63 | | (32) $false % 35.44/5.63 | | % 35.44/5.63 | | CLOSE: (32) is inconsistent. % 35.44/5.63 | | % 35.44/5.63 | Case 2: % 35.44/5.63 | | % 35.44/5.63 | | % 35.44/5.63 | | GROUND_INST: instantiating (13) with all_15_1, xx, all_15_0, xS, simplifying % 35.44/5.63 | | with (14), (15), (17), (18), (21), (24), (29) gives: % 35.44/5.63 | | (33) all_15_0 = xS | ? [v0: $i] : ($i(v0) & (v0 = xx | ~ % 35.44/5.63 | | aElementOf0(v0, all_15_1) | ~ aElementOf0(v0, xS) | ~ % 35.44/5.63 | | aElement0(v0)) & (aElementOf0(v0, xS) | ( ~ (v0 = xx) & % 35.44/5.63 | | aElementOf0(v0, all_15_1) & aElement0(v0)))) % 35.44/5.63 | | % 35.44/5.63 | | GROUND_INST: instantiating (10) with all_15_1, xx, all_15_0, simplifying % 35.44/5.63 | | with (15), (17), (21), (22), (24), (29) gives: % 35.44/5.64 | | (34) aSet0(all_15_0) % 35.44/5.64 | | % 35.44/5.64 | | GROUND_INST: instantiating (mConsDiff) with all_15_1, xx, all_15_0, % 35.44/5.64 | | simplifying with (17), (21), (24), (28), (29) gives: % 35.44/5.64 | | (35) sdtpldt0(all_15_0, xx) = all_15_1 % 35.44/5.64 | | % 35.44/5.64 | | GROUND_INST: instantiating (4) with xS, all_15_0, simplifying with (14), % 35.44/5.64 | | (18), (22), (34) gives: % 35.44/5.64 | | (36) aSubsetOf0(all_15_0, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 35.44/5.64 | | all_15_0) & ~ aElementOf0(v0, xS)) % 35.44/5.64 | | % 35.44/5.64 | | GROUND_INST: instantiating (4) with all_15_0, xS, simplifying with (14), % 35.44/5.64 | | (18), (22), (34) gives: % 35.44/5.64 | | (37) aSubsetOf0(xS, all_15_0) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 35.44/5.64 | | xS) & ~ aElementOf0(v0, all_15_0)) % 35.44/5.64 | | % 35.44/5.64 | | BETA: splitting (25) gives: % 35.44/5.64 | | % 35.44/5.64 | | Case 1: % 35.44/5.64 | | | % 35.44/5.64 | | | (38) ~ aSubsetOf0(all_15_0, xS) % 35.44/5.64 | | | % 35.44/5.64 | | | BETA: splitting (36) gives: % 35.44/5.64 | | | % 35.44/5.64 | | | Case 1: % 35.44/5.64 | | | | % 35.44/5.64 | | | | (39) aSubsetOf0(all_15_0, xS) % 35.44/5.64 | | | | % 35.44/5.64 | | | | PRED_UNIFY: (38), (39) imply: % 35.44/5.64 | | | | (40) $false % 35.44/5.64 | | | | % 35.44/5.64 | | | | CLOSE: (40) is inconsistent. % 35.44/5.64 | | | | % 35.44/5.64 | | | Case 2: % 35.44/5.64 | | | | % 35.44/5.64 | | | | (41) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_15_0) & ~ % 35.44/5.64 | | | | aElementOf0(v0, xS)) % 35.44/5.64 | | | | % 35.44/5.64 | | | | DELTA: instantiating (41) with fresh symbol all_105_0 gives: % 35.44/5.64 | | | | (42) $i(all_105_0) & aElementOf0(all_105_0, all_15_0) & ~ % 35.44/5.64 | | | | aElementOf0(all_105_0, xS) % 35.44/5.64 | | | | % 35.44/5.64 | | | | ALPHA: (42) implies: % 35.44/5.64 | | | | (43) ~ aElementOf0(all_105_0, xS) % 35.44/5.64 | | | | (44) aElementOf0(all_105_0, all_15_0) % 35.44/5.64 | | | | (45) $i(all_105_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | GROUND_INST: instantiating (12) with all_15_1, xx, all_15_0, all_105_0, % 35.44/5.64 | | | | simplifying with (15), (17), (21), (22), (24), (29), (44), % 35.44/5.64 | | | | (45) gives: % 35.44/5.64 | | | | (46) aElementOf0(all_105_0, all_15_1) % 35.44/5.64 | | | | % 35.44/5.64 | | | | GROUND_INST: instantiating (mEOfElem) with all_15_0, all_105_0, % 35.44/5.64 | | | | simplifying with (22), (34), (44), (45) gives: % 35.44/5.64 | | | | (47) aElement0(all_105_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | GROUND_INST: instantiating (8) with xS, xx, all_15_1, all_105_0, % 35.44/5.64 | | | | simplifying with (14), (15), (17), (18), (21), (23), (43), % 35.44/5.64 | | | | (45), (46) gives: % 35.44/5.64 | | | | (48) all_105_0 = xx % 35.44/5.64 | | | | % 35.44/5.64 | | | | REDUCE: (44), (48) imply: % 35.44/5.64 | | | | (49) aElementOf0(xx, all_15_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | GROUND_INST: instantiating (11) with all_15_1, xx, all_15_0, simplifying % 35.44/5.64 | | | | with (15), (17), (21), (22), (24), (29), (49) gives: % 35.44/5.64 | | | | (50) $false % 35.44/5.64 | | | | % 35.44/5.64 | | | | CLOSE: (50) is inconsistent. % 35.44/5.64 | | | | % 35.44/5.64 | | | End of split % 35.44/5.64 | | | % 35.44/5.64 | | Case 2: % 35.44/5.64 | | | % 35.44/5.64 | | | (51) ~ aSubsetOf0(xS, all_15_0) % 35.44/5.64 | | | % 35.44/5.64 | | | BETA: splitting (37) gives: % 35.44/5.64 | | | % 35.44/5.64 | | | Case 1: % 35.44/5.64 | | | | % 35.44/5.64 | | | | (52) aSubsetOf0(xS, all_15_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | PRED_UNIFY: (51), (52) imply: % 35.44/5.64 | | | | (53) $false % 35.44/5.64 | | | | % 35.44/5.64 | | | | CLOSE: (53) is inconsistent. % 35.44/5.64 | | | | % 35.44/5.64 | | | Case 2: % 35.44/5.64 | | | | % 35.44/5.64 | | | | (54) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & ~ aElementOf0(v0, % 35.44/5.64 | | | | all_15_0)) % 35.44/5.64 | | | | % 35.44/5.64 | | | | DELTA: instantiating (54) with fresh symbol all_105_0 gives: % 35.44/5.64 | | | | (55) $i(all_105_0) & aElementOf0(all_105_0, xS) & ~ % 35.44/5.64 | | | | aElementOf0(all_105_0, all_15_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | ALPHA: (55) implies: % 35.44/5.64 | | | | (56) ~ aElementOf0(all_105_0, all_15_0) % 35.44/5.64 | | | | (57) aElementOf0(all_105_0, xS) % 35.44/5.64 | | | | (58) $i(all_105_0) % 35.44/5.64 | | | | % 35.44/5.64 | | | | PRED_UNIFY: (16), (57) imply: % 35.44/5.65 | | | | (59) ~ (all_105_0 = xx) % 35.44/5.65 | | | | % 35.44/5.65 | | | | PRED_UNIFY: (56), (57) imply: % 35.44/5.65 | | | | (60) ~ (all_15_0 = xS) % 35.44/5.65 | | | | % 35.44/5.65 | | | | BETA: splitting (33) gives: % 35.44/5.65 | | | | % 35.44/5.65 | | | | Case 1: % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | (61) all_15_0 = xS % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | REDUCE: (60), (61) imply: % 35.44/5.65 | | | | | (62) $false % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | CLOSE: (62) is inconsistent. % 35.44/5.65 | | | | | % 35.44/5.65 | | | | Case 2: % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_105_0, simplifying % 35.44/5.65 | | | | | with (14), (18), (57), (58) gives: % 35.44/5.65 | | | | | (63) aElement0(all_105_0) % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | BETA: splitting (26) gives: % 35.44/5.65 | | | | | % 35.44/5.65 | | | | | Case 1: % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | GROUND_INST: instantiating (7) with xS, xx, all_15_1, all_105_0, % 35.44/5.65 | | | | | | simplifying with (14), (15), (17), (18), (21), (23), % 35.44/5.65 | | | | | | (57), (58), (63) gives: % 35.44/5.65 | | | | | | (64) aElementOf0(all_105_0, all_15_1) % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | GROUND_INST: instantiating (8) with all_15_0, xx, all_15_1, % 35.44/5.65 | | | | | | all_105_0, simplifying with (15), (17), (21), (22), % 35.44/5.65 | | | | | | (34), (35), (56), (58), (64) gives: % 35.44/5.65 | | | | | | (65) all_105_0 = xx % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | REDUCE: (59), (65) imply: % 35.44/5.65 | | | | | | (66) $false % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | CLOSE: (66) is inconsistent. % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | Case 2: % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | (67) ? [v0: $i] : ($i(v0) & aElementOf0(v0, slcrc0) & ~ % 35.44/5.65 | | | | | | aElementOf0(v0, xS)) % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | DELTA: instantiating (67) with fresh symbol all_143_0 gives: % 35.44/5.65 | | | | | | (68) $i(all_143_0) & aElementOf0(all_143_0, slcrc0) & ~ % 35.44/5.65 | | | | | | aElementOf0(all_143_0, xS) % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | ALPHA: (68) implies: % 35.44/5.65 | | | | | | (69) aElementOf0(all_143_0, slcrc0) % 35.44/5.65 | | | | | | (70) $i(all_143_0) % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | GROUND_INST: instantiating (2) with all_143_0, simplifying with % 35.44/5.65 | | | | | | (69), (70) gives: % 35.44/5.65 | | | | | | (71) $false % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | | CLOSE: (71) is inconsistent. % 35.44/5.65 | | | | | | % 35.44/5.65 | | | | | End of split % 35.44/5.65 | | | | | % 35.44/5.65 | | | | End of split % 35.44/5.65 | | | | % 35.44/5.65 | | | End of split % 35.44/5.65 | | | % 35.44/5.65 | | End of split % 35.44/5.65 | | % 35.44/5.65 | End of split % 35.44/5.65 | % 35.44/5.65 End of proof % 35.44/5.65 % SZS output end Proof for theBenchmark % 35.44/5.65 % 35.44/5.65 5005ms %------------------------------------------------------------------------------