%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM534+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 11:48:26 EDT 2023 % Result : Theorem 34.45s 5.34s % Output : Proof 34.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM534+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.35 % Computer : n020.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Fri Aug 25 16:04:00 EDT 2023 % 0.18/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.03/1.04 Prover 1: Preprocessing ... % 2.03/1.04 Prover 4: Preprocessing ... % 2.67/1.08 Prover 6: Preprocessing ... % 2.67/1.08 Prover 2: Preprocessing ... % 2.67/1.08 Prover 0: Preprocessing ... % 2.67/1.08 Prover 3: Preprocessing ... % 2.67/1.08 Prover 5: Preprocessing ... % 5.14/1.47 Prover 5: Constructing countermodel ... % 5.14/1.48 Prover 1: Constructing countermodel ... % 5.14/1.51 Prover 3: Constructing countermodel ... % 5.14/1.51 Prover 2: Proving ... % 5.14/1.55 Prover 6: Proving ... % 7.10/1.71 Prover 4: Constructing countermodel ... % 8.40/1.86 Prover 0: Proving ... % 9.13/1.95 Prover 3: gave up % 9.13/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.29/2.00 Prover 7: Preprocessing ... % 9.71/2.07 Prover 1: gave up % 9.71/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.71/2.11 Prover 7: Constructing countermodel ... % 9.71/2.15 Prover 8: Preprocessing ... % 10.50/2.23 Prover 8: Warning: ignoring some quantifiers % 10.50/2.24 Prover 8: Constructing countermodel ... % 13.59/2.56 Prover 8: gave up % 13.59/2.56 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 13.59/2.59 Prover 9: Preprocessing ... % 14.30/2.81 Prover 9: Constructing countermodel ... % 26.75/4.32 Prover 4: gave up % 26.75/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.08/4.35 Prover 10: Preprocessing ... % 27.08/4.42 Prover 10: Constructing countermodel ... % 34.45/5.34 Prover 10: Found proof (size 78) % 34.45/5.34 Prover 10: proved (1016ms) % 34.45/5.34 Prover 5: stopped % 34.45/5.34 Prover 7: stopped % 34.45/5.34 Prover 9: stopped % 34.45/5.34 Prover 2: stopped % 34.45/5.34 Prover 6: stopped % 34.45/5.34 Prover 0: stopped % 34.45/5.34 % 34.45/5.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 34.45/5.34 % 34.45/5.35 % SZS output start Proof for theBenchmark % 34.45/5.35 Assumptions after simplification: % 34.45/5.35 --------------------------------- % 34.45/5.35 % 34.45/5.35 (mCountNFin_01) % 34.45/5.35 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 34.45/5.35 % 34.45/5.35 (mDefCons) % 34.79/5.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 34.79/5.38 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 34.79/5.38 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 34.79/5.38 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 34.79/5.38 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = % 34.79/5.38 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.79/5.38 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ % 34.79/5.38 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | % 34.79/5.38 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.79/5.38 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 34.79/5.38 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 34.79/5.38 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 34.79/5.38 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 34.79/5.38 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ % 34.79/5.38 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.79/5.38 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 34.79/5.38 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1: % 34.79/5.38 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ % 34.79/5.38 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 34.79/5.38 % 34.79/5.38 (mDefDiff) % 34.79/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 34.79/5.39 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 34.79/5.39 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 34.79/5.39 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 34.79/5.39 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 34.79/5.39 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 34.79/5.39 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 34.79/5.39 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 34.79/5.39 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 34.79/5.39 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 34.79/5.39 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 34.79/5.39 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.79/5.39 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 34.79/5.39 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 34.79/5.39 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 34.79/5.39 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 34.79/5.39 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 34.79/5.39 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 34.79/5.39 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 34.79/5.39 % 34.79/5.39 (mDefEmp) % 34.79/5.39 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 34.79/5.39 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 34.79/5.39 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 34.79/5.39 % 34.79/5.39 (mDefSub) % 34.79/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 34.79/5.39 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 34.79/5.39 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 34.79/5.39 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 34.79/5.39 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 34.79/5.39 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 34.79/5.39 % 34.79/5.39 (mEOfElem) % 34.79/5.39 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 34.79/5.39 ~ aSet0(v0) | aElement0(v1)) % 34.79/5.39 % 34.79/5.39 (m__) % 34.79/5.39 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(xS, xx) % 34.79/5.39 = v0 & sdtpldt0(v0, xx) = v1 & $i(v1) & $i(v0)) % 34.79/5.39 % 34.79/5.39 (m__617) % 34.79/5.39 $i(xS) & aSet0(xS) % 34.79/5.39 % 34.79/5.39 (m__617_02) % 34.79/5.39 $i(xx) & $i(xS) & aElementOf0(xx, xS) % 34.79/5.39 % 34.79/5.39 Further assumptions not needed in the proof: % 34.79/5.39 -------------------------------------------- % 34.79/5.39 mCntRel, mCountNFin, mElmSort, mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, % 34.79/5.39 mSubRefl, mSubTrans % 34.79/5.39 % 34.79/5.39 Those formulas are unsatisfiable: % 34.79/5.39 --------------------------------- % 34.79/5.39 % 34.79/5.39 Begin of proof % 34.79/5.39 | % 34.79/5.39 | ALPHA: (mDefEmp) implies: % 34.79/5.39 | (1) aSet0(slcrc0) % 34.79/5.39 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 34.79/5.40 | (3) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] : % 34.79/5.40 | ($i(v1) & aElementOf0(v1, v0))) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (mCountNFin_01) implies: % 34.79/5.40 | (4) $i(slcrc0) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (mDefSub) implies: % 34.79/5.40 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 34.79/5.40 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 34.79/5.40 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 34.79/5.40 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 34.79/5.40 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 34.79/5.40 | aSet0(v0) | aElementOf0(v2, v0)) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (mDefCons) implies: % 34.79/5.40 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 34.79/5.40 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 34.79/5.40 | aSet0(v2)) % 34.79/5.40 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 34.79/5.40 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 34.79/5.40 | aElementOf0(v1, v2)) % 34.79/5.40 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 34.79/5.40 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 34.79/5.40 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & % 34.79/5.40 | ( ~ aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ % 34.79/5.40 | aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & % 34.79/5.40 | (v4 = v1 | aElementOf0(v4, v0)))))) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (mDefDiff) implies: % 34.79/5.40 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) % 34.79/5.40 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 34.79/5.40 | aSet0(v0) | aSet0(v2)) % 34.79/5.40 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) % 34.79/5.40 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~ % 34.79/5.40 | aElement0(v1) | ~ aSet0(v0)) % 34.79/5.40 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 34.79/5.40 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.79/5.40 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 34.79/5.40 | aElementOf0(v3, v0)) % 34.79/5.40 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 34.79/5.40 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.79/5.40 | $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 34.79/5.40 | aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (m__617) implies: % 34.79/5.40 | (14) aSet0(xS) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (m__617_02) implies: % 34.79/5.40 | (15) aElementOf0(xx, xS) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (m__) implies: % 34.79/5.40 | (16) $i(xS) % 34.79/5.40 | (17) $i(xx) % 34.79/5.40 | (18) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(xS, xx) = v0 & % 34.79/5.40 | sdtpldt0(v0, xx) = v1 & $i(v1) & $i(v0)) % 34.79/5.40 | % 34.79/5.40 | DELTA: instantiating (18) with fresh symbols all_14_0, all_14_1 gives: % 34.79/5.40 | (19) ~ (all_14_0 = xS) & sdtmndt0(xS, xx) = all_14_1 & sdtpldt0(all_14_1, % 34.79/5.40 | xx) = all_14_0 & $i(all_14_0) & $i(all_14_1) % 34.79/5.40 | % 34.79/5.40 | ALPHA: (19) implies: % 34.79/5.40 | (20) ~ (all_14_0 = xS) % 34.79/5.40 | (21) $i(all_14_1) % 34.79/5.40 | (22) $i(all_14_0) % 34.79/5.40 | (23) sdtpldt0(all_14_1, xx) = all_14_0 % 34.79/5.40 | (24) sdtmndt0(xS, xx) = all_14_1 % 34.79/5.40 | % 34.79/5.41 | GROUND_INST: instantiating (mEOfElem) with xS, xx, simplifying with (14), % 34.79/5.41 | (15), (16), (17) gives: % 34.79/5.41 | (25) aElement0(xx) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (10) with xS, xx, all_14_1, simplifying with (14), % 34.79/5.41 | (16), (17), (21), (24), (25) gives: % 34.79/5.41 | (26) aSet0(all_14_1) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (9) with all_14_1, xx, all_14_0, xS, simplifying % 34.79/5.41 | with (14), (16), (17), (21), (23), (25), (26) gives: % 34.79/5.41 | (27) all_14_0 = xS | ? [v0: $i] : ($i(v0) & ( ~ aElementOf0(v0, xS) | ~ % 34.79/5.41 | aElement0(v0) | ( ~ (v0 = xx) & ~ aElementOf0(v0, all_14_1))) & % 34.79/5.41 | (aElementOf0(v0, xS) | (aElement0(v0) & (v0 = xx | aElementOf0(v0, % 34.79/5.41 | all_14_1))))) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (9) with all_14_1, xx, all_14_0, slcrc0, % 34.79/5.41 | simplifying with (1), (4), (17), (21), (23), (25), (26) gives: % 34.79/5.41 | (28) all_14_0 = slcrc0 | ? [v0: $i] : ($i(v0) & ( ~ aElementOf0(v0, % 34.79/5.41 | slcrc0) | ~ aElement0(v0) | ( ~ (v0 = xx) & ~ aElementOf0(v0, % 34.79/5.41 | all_14_1))) & (aElementOf0(v0, slcrc0) | (aElement0(v0) & (v0 % 34.79/5.41 | = xx | aElementOf0(v0, all_14_1))))) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (8) with all_14_1, xx, all_14_0, simplifying with % 34.79/5.41 | (17), (21), (22), (23), (25), (26) gives: % 34.79/5.41 | (29) aElementOf0(xx, all_14_0) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (7) with all_14_1, xx, all_14_0, simplifying with % 34.79/5.41 | (17), (21), (22), (23), (25), (26) gives: % 34.79/5.41 | (30) aSet0(all_14_0) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (5) with xS, all_14_1, simplifying with (14), (16), % 34.79/5.41 | (21), (26) gives: % 34.79/5.41 | (31) aSubsetOf0(all_14_1, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 34.79/5.41 | all_14_1) & ~ aElementOf0(v0, xS)) % 34.79/5.41 | % 34.79/5.41 | GROUND_INST: instantiating (5) with all_14_1, xS, simplifying with (14), (16), % 34.79/5.41 | (21), (26) gives: % 34.79/5.41 | (32) aSubsetOf0(xS, all_14_1) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) % 34.79/5.41 | & ~ aElementOf0(v0, all_14_1)) % 34.79/5.41 | % 34.79/5.41 | BETA: splitting (27) gives: % 34.79/5.41 | % 34.79/5.41 | Case 1: % 34.79/5.41 | | % 34.79/5.41 | | (33) all_14_0 = xS % 34.79/5.41 | | % 34.79/5.41 | | REDUCE: (20), (33) imply: % 34.79/5.41 | | (34) $false % 34.79/5.41 | | % 34.79/5.41 | | CLOSE: (34) is inconsistent. % 34.79/5.41 | | % 34.79/5.41 | Case 2: % 34.79/5.41 | | % 34.79/5.41 | | (35) ? [v0: $i] : ($i(v0) & ( ~ aElementOf0(v0, xS) | ~ aElement0(v0) | % 34.79/5.41 | | ( ~ (v0 = xx) & ~ aElementOf0(v0, all_14_1))) & % 34.79/5.41 | | (aElementOf0(v0, xS) | (aElement0(v0) & (v0 = xx | aElementOf0(v0, % 34.79/5.41 | | all_14_1))))) % 34.79/5.41 | | % 34.79/5.41 | | DELTA: instantiating (35) with fresh symbol all_42_0 gives: % 34.79/5.41 | | (36) $i(all_42_0) & ( ~ aElementOf0(all_42_0, xS) | ~ % 34.79/5.41 | | aElement0(all_42_0) | ( ~ (all_42_0 = xx) & ~ % 34.79/5.41 | | aElementOf0(all_42_0, all_14_1))) & (aElementOf0(all_42_0, xS) | % 34.79/5.41 | | (aElement0(all_42_0) & (all_42_0 = xx | aElementOf0(all_42_0, % 34.79/5.41 | | all_14_1)))) % 34.79/5.41 | | % 34.79/5.41 | | ALPHA: (36) implies: % 34.79/5.42 | | (37) $i(all_42_0) % 34.79/5.42 | | (38) aElementOf0(all_42_0, xS) | (aElement0(all_42_0) & (all_42_0 = xx | % 34.79/5.42 | | aElementOf0(all_42_0, all_14_1))) % 34.79/5.42 | | (39) ~ aElementOf0(all_42_0, xS) | ~ aElement0(all_42_0) | ( ~ % 34.79/5.42 | | (all_42_0 = xx) & ~ aElementOf0(all_42_0, all_14_1)) % 34.79/5.42 | | % 34.79/5.42 | | GROUND_INST: instantiating (3) with all_14_0, simplifying with (22), (30) % 34.79/5.42 | | gives: % 34.79/5.42 | | (40) all_14_0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 34.79/5.42 | | all_14_0)) % 34.79/5.42 | | % 34.79/5.42 | | BETA: splitting (31) gives: % 34.79/5.42 | | % 34.79/5.42 | | Case 1: % 34.79/5.42 | | | % 34.79/5.42 | | | (41) aSubsetOf0(all_14_1, xS) % 34.79/5.42 | | | % 34.79/5.42 | | | BETA: splitting (32) gives: % 34.79/5.42 | | | % 34.79/5.42 | | | Case 1: % 34.79/5.42 | | | | % 34.79/5.42 | | | | (42) aSubsetOf0(xS, all_14_1) % 34.79/5.42 | | | | % 34.79/5.42 | | | | BETA: splitting (28) gives: % 34.79/5.42 | | | | % 34.79/5.42 | | | | Case 1: % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | (43) all_14_0 = slcrc0 % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | REDUCE: (29), (43) imply: % 34.79/5.42 | | | | | (44) aElementOf0(xx, slcrc0) % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | GROUND_INST: instantiating (2) with xx, simplifying with (17), (44) % 34.79/5.42 | | | | | gives: % 34.79/5.42 | | | | | (45) $false % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | CLOSE: (45) is inconsistent. % 34.79/5.42 | | | | | % 34.79/5.42 | | | | Case 2: % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | (46) ~ (all_14_0 = slcrc0) % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | BETA: splitting (40) gives: % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | Case 1: % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | (47) all_14_0 = slcrc0 % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | REDUCE: (46), (47) imply: % 34.79/5.42 | | | | | | (48) $false % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | CLOSE: (48) is inconsistent. % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | Case 2: % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | GROUND_INST: instantiating (6) with all_14_1, xS, xx, simplifying % 34.79/5.42 | | | | | | with (15), (16), (17), (21), (26), (42) gives: % 34.79/5.42 | | | | | | (49) aElementOf0(xx, all_14_1) % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | GROUND_INST: instantiating (11) with xS, xx, all_14_1, simplifying % 34.79/5.42 | | | | | | with (14), (16), (17), (21), (24), (25), (49) gives: % 34.79/5.42 | | | | | | (50) $false % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | CLOSE: (50) is inconsistent. % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | End of split % 34.79/5.42 | | | | | % 34.79/5.42 | | | | End of split % 34.79/5.42 | | | | % 34.79/5.42 | | | Case 2: % 34.79/5.42 | | | | % 34.79/5.42 | | | | (51) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & ~ aElementOf0(v0, % 34.79/5.42 | | | | all_14_1)) % 34.79/5.42 | | | | % 34.79/5.42 | | | | DELTA: instantiating (51) with fresh symbol all_160_0 gives: % 34.79/5.42 | | | | (52) $i(all_160_0) & aElementOf0(all_160_0, xS) & ~ % 34.79/5.42 | | | | aElementOf0(all_160_0, all_14_1) % 34.79/5.42 | | | | % 34.79/5.42 | | | | ALPHA: (52) implies: % 34.79/5.42 | | | | (53) ~ aElementOf0(all_160_0, all_14_1) % 34.79/5.42 | | | | (54) aElementOf0(all_160_0, xS) % 34.79/5.42 | | | | (55) $i(all_160_0) % 34.79/5.42 | | | | % 34.79/5.42 | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_160_0, simplifying % 34.79/5.42 | | | | with (14), (16), (54), (55) gives: % 34.79/5.42 | | | | (56) aElement0(all_160_0) % 34.79/5.42 | | | | % 34.79/5.42 | | | | BETA: splitting (38) gives: % 34.79/5.42 | | | | % 34.79/5.42 | | | | Case 1: % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | (57) aElementOf0(all_42_0, xS) % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | BETA: splitting (39) gives: % 34.79/5.42 | | | | | % 34.79/5.42 | | | | | Case 1: % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | (58) ~ aElementOf0(all_42_0, xS) % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | PRED_UNIFY: (57), (58) imply: % 34.79/5.42 | | | | | | (59) $false % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | CLOSE: (59) is inconsistent. % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | Case 2: % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | (60) ~ aElement0(all_42_0) | ( ~ (all_42_0 = xx) & ~ % 34.79/5.42 | | | | | | aElementOf0(all_42_0, all_14_1)) % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | GROUND_INST: instantiating (13) with xS, xx, all_14_1, all_160_0, % 34.79/5.42 | | | | | | simplifying with (14), (16), (17), (21), (24), (25), % 34.79/5.42 | | | | | | (53), (54), (55), (56) gives: % 34.79/5.42 | | | | | | (61) all_160_0 = xx % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_42_0, simplifying % 34.79/5.42 | | | | | | with (14), (16), (37), (57) gives: % 34.79/5.42 | | | | | | (62) aElement0(all_42_0) % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | BETA: splitting (60) gives: % 34.79/5.42 | | | | | | % 34.79/5.42 | | | | | | Case 1: % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | | (63) ~ aElement0(all_42_0) % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | | PRED_UNIFY: (62), (63) imply: % 34.79/5.42 | | | | | | | (64) $false % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | | CLOSE: (64) is inconsistent. % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | Case 2: % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | | (65) ~ (all_42_0 = xx) & ~ aElementOf0(all_42_0, all_14_1) % 34.79/5.42 | | | | | | | % 34.79/5.42 | | | | | | | ALPHA: (65) implies: % 34.79/5.43 | | | | | | | (66) ~ (all_42_0 = xx) % 34.79/5.43 | | | | | | | (67) ~ aElementOf0(all_42_0, all_14_1) % 34.79/5.43 | | | | | | | % 34.79/5.43 | | | | | | | GROUND_INST: instantiating (13) with xS, xx, all_14_1, all_42_0, % 34.79/5.43 | | | | | | | simplifying with (14), (16), (17), (21), (24), (25), % 34.79/5.43 | | | | | | | (37), (57), (62), (67) gives: % 34.79/5.43 | | | | | | | (68) all_42_0 = xx % 34.79/5.43 | | | | | | | % 34.79/5.43 | | | | | | | REDUCE: (66), (68) imply: % 34.79/5.43 | | | | | | | (69) $false % 34.79/5.43 | | | | | | | % 34.79/5.43 | | | | | | | CLOSE: (69) is inconsistent. % 34.79/5.43 | | | | | | | % 34.79/5.43 | | | | | | End of split % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | End of split % 34.79/5.43 | | | | | % 34.79/5.43 | | | | Case 2: % 34.79/5.43 | | | | | % 34.79/5.43 | | | | | (70) ~ aElementOf0(all_42_0, xS) % 34.79/5.43 | | | | | (71) aElement0(all_42_0) & (all_42_0 = xx | aElementOf0(all_42_0, % 34.79/5.43 | | | | | all_14_1)) % 34.79/5.43 | | | | | % 34.79/5.43 | | | | | ALPHA: (71) implies: % 34.79/5.43 | | | | | (72) all_42_0 = xx | aElementOf0(all_42_0, all_14_1) % 34.79/5.43 | | | | | % 34.79/5.43 | | | | | BETA: splitting (72) gives: % 34.79/5.43 | | | | | % 34.79/5.43 | | | | | Case 1: % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | (73) aElementOf0(all_42_0, all_14_1) % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | GROUND_INST: instantiating (6) with xS, all_14_1, all_42_0, % 34.79/5.43 | | | | | | simplifying with (14), (16), (21), (37), (41), (70), % 34.79/5.43 | | | | | | (73) gives: % 34.79/5.43 | | | | | | (74) $false % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | CLOSE: (74) is inconsistent. % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | Case 2: % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | (75) all_42_0 = xx % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | REDUCE: (70), (75) imply: % 34.79/5.43 | | | | | | (76) ~ aElementOf0(xx, xS) % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | PRED_UNIFY: (15), (76) imply: % 34.79/5.43 | | | | | | (77) $false % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | | CLOSE: (77) is inconsistent. % 34.79/5.43 | | | | | | % 34.79/5.43 | | | | | End of split % 34.79/5.43 | | | | | % 34.79/5.43 | | | | End of split % 34.79/5.43 | | | | % 34.79/5.43 | | | End of split % 34.79/5.43 | | | % 34.79/5.43 | | Case 2: % 34.79/5.43 | | | % 34.79/5.43 | | | (78) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_14_1) & ~ % 34.79/5.43 | | | aElementOf0(v0, xS)) % 34.79/5.43 | | | % 34.79/5.43 | | | DELTA: instantiating (78) with fresh symbol all_146_0 gives: % 34.79/5.43 | | | (79) $i(all_146_0) & aElementOf0(all_146_0, all_14_1) & ~ % 34.79/5.43 | | | aElementOf0(all_146_0, xS) % 34.79/5.43 | | | % 34.79/5.43 | | | ALPHA: (79) implies: % 34.79/5.43 | | | (80) ~ aElementOf0(all_146_0, xS) % 34.79/5.43 | | | (81) aElementOf0(all_146_0, all_14_1) % 34.79/5.43 | | | (82) $i(all_146_0) % 34.79/5.43 | | | % 34.79/5.43 | | | GROUND_INST: instantiating (12) with xS, xx, all_14_1, all_146_0, % 34.79/5.43 | | | simplifying with (14), (16), (17), (21), (24), (25), (80), % 34.79/5.43 | | | (81), (82) gives: % 34.79/5.43 | | | (83) $false % 34.79/5.43 | | | % 34.79/5.43 | | | CLOSE: (83) is inconsistent. % 34.79/5.43 | | | % 34.79/5.43 | | End of split % 34.79/5.43 | | % 34.79/5.43 | End of split % 34.79/5.43 | % 34.79/5.43 End of proof % 34.79/5.43 % SZS output end Proof for theBenchmark % 34.79/5.43 % 34.79/5.43 4818ms %------------------------------------------------------------------------------