%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM536+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 14.07s 2.58s % Output : Proof 15.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUM536+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n019.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Aug 25 10:33:28 EDT 2023 % 0.11/0.33 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.22/1.03 Prover 1: Preprocessing ... % 2.22/1.05 Prover 4: Preprocessing ... % 2.89/1.07 Prover 3: Preprocessing ... % 2.89/1.07 Prover 2: Preprocessing ... % 2.89/1.07 Prover 0: Preprocessing ... % 2.89/1.07 Prover 5: Preprocessing ... % 2.89/1.07 Prover 6: Preprocessing ... % 5.67/1.54 Prover 1: Constructing countermodel ... % 5.67/1.54 Prover 5: Constructing countermodel ... % 6.55/1.56 Prover 3: Constructing countermodel ... % 6.55/1.58 Prover 2: Proving ... % 6.55/1.58 Prover 6: Proving ... % 7.89/1.75 Prover 4: Constructing countermodel ... % 8.75/1.87 Prover 0: Proving ... % 14.07/2.58 Prover 3: proved (1945ms) % 14.07/2.58 % 14.07/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.07/2.58 % 14.07/2.58 Prover 6: stopped % 14.07/2.59 Prover 5: stopped % 14.07/2.60 Prover 2: stopped % 14.07/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.07/2.60 Prover 0: stopped % 14.07/2.62 Prover 1: Found proof (size 119) % 14.07/2.62 Prover 1: proved (1964ms) % 14.07/2.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.07/2.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.07/2.62 Prover 7: Preprocessing ... % 14.07/2.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.07/2.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.07/2.62 Prover 4: stopped % 14.07/2.62 Prover 7: stopped % 14.07/2.62 Prover 10: Preprocessing ... % 14.07/2.63 Prover 8: Preprocessing ... % 14.07/2.64 Prover 10: stopped % 14.64/2.66 Prover 11: Preprocessing ... % 14.64/2.66 Prover 13: Preprocessing ... % 14.77/2.68 Prover 13: stopped % 14.77/2.70 Prover 11: stopped % 14.77/2.71 Prover 8: Warning: ignoring some quantifiers % 14.77/2.71 Prover 8: Constructing countermodel ... % 14.77/2.71 Prover 8: stopped % 14.77/2.71 % 14.77/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.77/2.71 % 14.77/2.72 % SZS output start Proof for theBenchmark % 14.77/2.73 Assumptions after simplification: % 14.77/2.73 --------------------------------- % 14.77/2.73 % 14.77/2.73 (mDefCons) % 14.77/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 14.77/2.76 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aSet0(v0) = v3 & % 14.77/2.76 aElement0(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ( ! [v3: $i] : (v3 = % 14.77/2.76 v2 | ~ (aSet0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : ? % 14.77/2.76 [v6: any] : ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v3) = % 14.77/2.76 v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 14.77/2.76 ( ~ (v7 = 0) & ~ (v4 = v1))) & (v5 = 0 | (v6 = 0 & (v7 = 0 | v4 = % 14.77/2.76 v1))))) & ! [v3: any] : ( ~ (aSet0(v2) = v3) | ~ $i(v2) | (v3 % 14.77/2.76 = 0 & ! [v4: $i] : ! [v5: any] : ( ~ (aElement0(v4) = v5) | ~ % 14.77/2.76 $i(v4) | ? [v6: any] : ? [v7: any] : (aElementOf0(v4, v2) = v6 & % 14.77/2.76 aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v5 = 0 & (v7 = 0 | v4 = % 14.77/2.76 v1))))) & ! [v4: $i] : ( ~ (aElement0(v4) = 0) | ~ $i(v4) % 14.77/2.76 | ? [v5: any] : ? [v6: any] : (aElementOf0(v4, v2) = v6 & % 14.77/2.76 aElementOf0(v4, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 14.77/2.76 v1))))))))) % 14.77/2.76 % 14.77/2.76 (mDefDiff) % 14.77/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ % 14.77/2.77 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aSet0(v0) = v3 & % 14.77/2.77 aElement0(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ( ! [v3: $i] : (v3 = % 14.77/2.77 v2 | ~ (aSet0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : ? % 14.77/2.77 [v6: any] : ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v3) = % 14.77/2.77 v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 14.77/2.77 ~ (v5 = 0) | v4 = v1) & (v5 = 0 | (v7 = 0 & v6 = 0 & ~ (v4 = % 14.77/2.77 v1))))) & ! [v3: any] : ( ~ (aSet0(v2) = v3) | ~ $i(v2) | (v3 % 14.77/2.77 = 0 & ! [v4: $i] : ! [v5: any] : ( ~ (aElement0(v4) = v5) | ~ % 14.77/2.77 $i(v4) | ? [v6: any] : ? [v7: any] : (aElementOf0(v4, v2) = v6 & % 14.77/2.77 aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v7 = 0 & v5 = 0 & ~ % 14.77/2.77 (v4 = v1))))) & ! [v4: $i] : (v4 = v1 | ~ (aElement0(v4) = % 14.77/2.77 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (aElementOf0(v4, % 14.77/2.77 v2) = v6 & aElementOf0(v4, v0) = v5 & ( ~ (v5 = 0) | v6 = % 14.77/2.77 0))))))) % 14.77/2.77 % 14.77/2.77 (mEOfElem) % 14.77/2.77 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : % 14.77/2.77 (v2 = 0 | ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 14.77/2.77 & aElementOf0(v1, v0) = v3))) % 14.77/2.77 % 14.77/2.77 (m__) % 14.77/2.77 $i(xS) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) % 14.77/2.77 = v1 & sdtpldt0(xS, xx) = v0 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) & % 14.77/2.77 $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = xx | ~ % 14.77/2.77 (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 14.77/2.77 (aElement0(v2) = v4 & aElementOf0(v2, v0) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 14.77/2.77 0)))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 14.77/2.77 v0) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (aElement0(v2) = % 14.77/2.77 v4 & aElementOf0(v2, xS) = v5 & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v2 = % 14.77/2.77 xx))))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) | ~ $i(v2) % 14.77/2.77 | ( ~ (v2 = xx) & aElement0(v2) = 0 & aElementOf0(v2, v0) = 0)) & ! [v2: % 14.77/2.77 $i] : ( ~ (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: any] : % 14.77/2.77 (aElement0(v2) = 0 & aElementOf0(v2, xS) = v3 & (v3 = 0 | v2 = xx)))) % 14.77/2.77 % 14.77/2.77 (m__679) % 14.77/2.77 aSet0(xS) = 0 & aElement0(xx) = 0 & $i(xS) & $i(xx) % 14.77/2.77 % 14.77/2.77 (m__679_02) % 14.77/2.77 $i(xS) & $i(xx) & ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xS) = v0) % 14.77/2.77 % 14.77/2.77 (function-axioms) % 14.77/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.77/2.78 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 14.77/2.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 14.77/2.78 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.77/2.78 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.77/2.78 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 14.77/2.78 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.77/2.78 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 14.77/2.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 14.77/2.78 v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & ! [v0: % 14.77/2.78 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.77/2.78 ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 14.77/2.78 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.77/2.78 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.77/2.78 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 14.77/2.78 ~ (aElement0(v2) = v0)) % 14.77/2.78 % 14.77/2.78 Further assumptions not needed in the proof: % 14.77/2.78 -------------------------------------------- % 14.77/2.78 mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefEmp, mDefSub, mElmSort, % 14.77/2.78 mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans % 14.77/2.78 % 14.77/2.78 Those formulas are unsatisfiable: % 14.77/2.78 --------------------------------- % 14.77/2.78 % 14.77/2.78 Begin of proof % 14.77/2.78 | % 14.77/2.78 | ALPHA: (m__679) implies: % 14.77/2.78 | (1) aElement0(xx) = 0 % 14.77/2.78 | (2) aSet0(xS) = 0 % 14.77/2.78 | % 14.77/2.78 | ALPHA: (m__679_02) implies: % 14.77/2.78 | (3) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xS) = v0) % 14.77/2.78 | % 14.77/2.78 | ALPHA: (m__) implies: % 14.77/2.78 | (4) $i(xx) % 14.77/2.78 | (5) $i(xS) % 14.77/2.78 | (6) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) = v1 & % 14.77/2.78 | sdtpldt0(xS, xx) = v0 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) & % 14.77/2.78 | $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = xx | ~ % 14.77/2.78 | (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 14.77/2.78 | any] : (aElement0(v2) = v4 & aElementOf0(v2, v0) = v5 & ( ~ (v5 = % 14.77/2.78 | 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 14.77/2.78 | ~ (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 14.77/2.78 | any] : (aElement0(v2) = v4 & aElementOf0(v2, xS) = v5 & ( ~ (v4 = % 14.77/2.78 | 0) | ( ~ (v5 = 0) & ~ (v2 = xx))))) & ! [v2: $i] : ( ~ % 14.77/2.78 | (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ( ~ (v2 = xx) & % 14.77/2.78 | aElement0(v2) = 0 & aElementOf0(v2, v0) = 0)) & ! [v2: $i] : ( ~ % 14.77/2.78 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: any] : % 14.77/2.78 | (aElement0(v2) = 0 & aElementOf0(v2, xS) = v3 & (v3 = 0 | v2 = % 14.77/2.78 | xx)))) % 14.77/2.78 | % 14.77/2.78 | ALPHA: (function-axioms) implies: % 14.77/2.79 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.77/2.79 | (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 14.77/2.79 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.77/2.79 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 14.77/2.79 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.77/2.79 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 14.77/2.79 | (aElementOf0(v3, v2) = v0)) % 14.77/2.79 | % 14.77/2.79 | DELTA: instantiating (3) with fresh symbol all_15_0 gives: % 14.77/2.79 | (10) ~ (all_15_0 = 0) & aElementOf0(xx, xS) = all_15_0 % 14.77/2.79 | % 14.77/2.79 | ALPHA: (10) implies: % 14.77/2.79 | (11) ~ (all_15_0 = 0) % 14.77/2.79 | (12) aElementOf0(xx, xS) = all_15_0 % 14.77/2.79 | % 14.77/2.79 | DELTA: instantiating (6) with fresh symbols all_17_0, all_17_1 gives: % 14.77/2.79 | (13) ~ (all_17_0 = xS) & sdtmndt0(all_17_1, xx) = all_17_0 & sdtpldt0(xS, % 14.77/2.79 | xx) = all_17_1 & aSet0(all_17_0) = 0 & aSet0(all_17_1) = 0 & % 14.77/2.79 | $i(all_17_0) & $i(all_17_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 14.77/2.79 | v0 = xx | ~ (aElementOf0(v0, all_17_0) = v1) | ~ $i(v0) | ? [v2: % 14.77/2.79 | any] : ? [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0, % 14.77/2.79 | all_17_1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : % 14.77/2.79 | ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_17_1) = v1) | ~ % 14.77/2.79 | $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = v2 & % 14.77/2.79 | aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ (v0 = % 14.77/2.79 | xx))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_17_0) = 0) % 14.77/2.79 | | ~ $i(v0) | ( ~ (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0, % 14.77/2.79 | all_17_1) = 0)) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_17_1) = % 14.77/2.79 | 0) | ~ $i(v0) | ? [v1: any] : (aElement0(v0) = 0 & % 14.77/2.79 | aElementOf0(v0, xS) = v1 & (v1 = 0 | v0 = xx))) % 14.77/2.79 | % 14.77/2.79 | ALPHA: (13) implies: % 14.77/2.79 | (14) ~ (all_17_0 = xS) % 14.77/2.79 | (15) $i(all_17_1) % 14.77/2.79 | (16) $i(all_17_0) % 14.77/2.79 | (17) aSet0(all_17_1) = 0 % 14.77/2.79 | (18) aSet0(all_17_0) = 0 % 14.77/2.79 | (19) sdtpldt0(xS, xx) = all_17_1 % 14.77/2.79 | (20) sdtmndt0(all_17_1, xx) = all_17_0 % 14.77/2.79 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_17_1) = % 14.77/2.79 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = % 14.77/2.79 | v2 & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ % 14.77/2.79 | (v0 = xx))))) % 14.77/2.79 | % 14.77/2.79 | GROUND_INST: instantiating (mEOfElem) with xS, simplifying with (2), (5) % 14.77/2.79 | gives: % 14.77/2.79 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElement0(v0) = v1) | ~ % 14.77/2.79 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xS) = v2)) % 14.77/2.79 | % 14.77/2.79 | GROUND_INST: instantiating (mDefCons) with xS, xx, all_17_1, simplifying with % 14.77/2.79 | (4), (5), (19) gives: % 14.77/2.80 | (23) ? [v0: any] : ? [v1: any] : (aSet0(xS) = v0 & aElement0(xx) = v1 & ( % 14.77/2.80 | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: any] : (v0 = all_17_1 | ~ % 14.77/2.80 | (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: % 14.77/2.80 | any] : ? [v4: any] : (aElement0(v1) = v3 & aElementOf0(v1, v0) % 14.77/2.80 | = v2 & aElementOf0(v1, xS) = v4 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 % 14.77/2.80 | = 0) | ( ~ (v4 = 0) & ~ (v1 = xx))) & (v2 = 0 | (v3 = 0 & % 14.77/2.80 | (v4 = 0 | v1 = xx))))) & ! [v0: any] : ( ~ (aSet0(all_17_1) % 14.77/2.80 | = v0) | ~ $i(all_17_1) | (v0 = 0 & ! [v1: $i] : ! [v2: any] : % 14.77/2.80 | ( ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 14.77/2.80 | any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1, xS) % 14.77/2.80 | = v4 & ( ~ (v3 = 0) | (v2 = 0 & (v4 = 0 | v1 = xx))))) & ! % 14.77/2.80 | [v1: $i] : ( ~ (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : % 14.77/2.80 | ? [v3: any] : (aElementOf0(v1, all_17_1) = v3 & % 14.77/2.80 | aElementOf0(v1, xS) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = % 14.77/2.80 | xx)))))))) % 14.77/2.80 | % 14.77/2.80 | GROUND_INST: instantiating (mDefDiff) with all_17_1, xx, all_17_0, simplifying % 14.77/2.80 | with (4), (15), (20) gives: % 14.77/2.80 | (24) ? [v0: any] : ? [v1: any] : (aSet0(all_17_1) = v0 & aElement0(xx) = % 14.77/2.80 | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: any] : (v0 = all_17_0 | % 14.77/2.80 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? % 14.77/2.80 | [v3: any] : ? [v4: any] : (aElement0(v1) = v3 & aElementOf0(v1, % 14.77/2.80 | v0) = v2 & aElementOf0(v1, all_17_1) = v4 & $i(v1) & ( ~ (v4 = % 14.77/2.80 | 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = xx) & (v2 = 0 | (v4 = % 14.77/2.80 | 0 & v3 = 0 & ~ (v1 = xx))))) & ! [v0: any] : ( ~ % 14.77/2.80 | (aSet0(all_17_0) = v0) | ~ $i(all_17_0) | (v0 = 0 & ! [v1: $i] : % 14.77/2.80 | ! [v2: any] : ( ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: % 14.77/2.80 | any] : ? [v4: any] : (aElementOf0(v1, all_17_0) = v3 & % 14.77/2.80 | aElementOf0(v1, all_17_1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 % 14.77/2.80 | = 0 & ~ (v1 = xx))))) & ! [v1: $i] : (v1 = xx | ~ % 14.77/2.80 | (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] % 14.77/2.80 | : (aElementOf0(v1, all_17_0) = v3 & aElementOf0(v1, all_17_1) % 14.77/2.80 | = v2 & ( ~ (v2 = 0) | v3 = 0)))))) % 14.77/2.80 | % 14.77/2.80 | BETA: splitting (24) gives: % 14.77/2.80 | % 14.77/2.80 | Case 1: % 14.77/2.80 | | % 14.77/2.80 | | (25) ? [v0: any] : ? [v1: any] : (aSet0(all_17_1) = v0 & aElement0(xx) % 14.77/2.80 | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.77/2.80 | | % 14.77/2.80 | | DELTA: instantiating (25) with fresh symbols all_39_0, all_39_1 gives: % 14.77/2.80 | | (26) aSet0(all_17_1) = all_39_1 & aElement0(xx) = all_39_0 & ( ~ % 14.77/2.80 | | (all_39_0 = 0) | ~ (all_39_1 = 0)) % 14.77/2.80 | | % 14.77/2.80 | | ALPHA: (26) implies: % 14.77/2.80 | | (27) aElement0(xx) = all_39_0 % 14.77/2.80 | | (28) aSet0(all_17_1) = all_39_1 % 14.77/2.80 | | (29) ~ (all_39_0 = 0) | ~ (all_39_1 = 0) % 14.77/2.80 | | % 14.77/2.80 | | GROUND_INST: instantiating (7) with 0, all_39_0, xx, simplifying with (1), % 14.77/2.80 | | (27) gives: % 14.77/2.80 | | (30) all_39_0 = 0 % 14.77/2.80 | | % 14.77/2.80 | | GROUND_INST: instantiating (8) with 0, all_39_1, all_17_1, simplifying with % 14.77/2.80 | | (17), (28) gives: % 14.77/2.80 | | (31) all_39_1 = 0 % 14.77/2.80 | | % 14.77/2.80 | | BETA: splitting (29) gives: % 14.77/2.80 | | % 14.77/2.80 | | Case 1: % 14.77/2.80 | | | % 14.77/2.80 | | | (32) ~ (all_39_0 = 0) % 14.77/2.80 | | | % 14.77/2.80 | | | REDUCE: (30), (32) imply: % 14.77/2.81 | | | (33) $false % 14.77/2.81 | | | % 14.77/2.81 | | | CLOSE: (33) is inconsistent. % 14.77/2.81 | | | % 14.77/2.81 | | Case 2: % 14.77/2.81 | | | % 14.77/2.81 | | | (34) ~ (all_39_1 = 0) % 14.77/2.81 | | | % 14.77/2.81 | | | REDUCE: (31), (34) imply: % 14.77/2.81 | | | (35) $false % 14.77/2.81 | | | % 14.77/2.81 | | | CLOSE: (35) is inconsistent. % 14.77/2.81 | | | % 14.77/2.81 | | End of split % 14.77/2.81 | | % 14.77/2.81 | Case 2: % 14.77/2.81 | | % 14.77/2.81 | | (36) ! [v0: any] : (v0 = all_17_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? % 14.77/2.81 | | [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] : % 14.77/2.81 | | (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1, % 14.77/2.81 | | all_17_1) = v4 & $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 % 14.77/2.81 | | = 0) | v1 = xx) & (v2 = 0 | (v4 = 0 & v3 = 0 & ~ (v1 = % 14.77/2.81 | | xx))))) & ! [v0: any] : ( ~ (aSet0(all_17_0) = v0) | ~ % 14.77/2.81 | | $i(all_17_0) | (v0 = 0 & ! [v1: $i] : ! [v2: any] : ( ~ % 14.77/2.81 | | (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] % 14.77/2.81 | | : (aElementOf0(v1, all_17_0) = v3 & aElementOf0(v1, all_17_1) % 14.77/2.81 | | = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0 & ~ (v1 = xx))))) & % 14.77/2.81 | | ! [v1: $i] : (v1 = xx | ~ (aElement0(v1) = 0) | ~ $i(v1) | ? % 14.77/2.81 | | [v2: any] : ? [v3: any] : (aElementOf0(v1, all_17_0) = v3 & % 14.77/2.81 | | aElementOf0(v1, all_17_1) = v2 & ( ~ (v2 = 0) | v3 = 0))))) % 14.77/2.81 | | % 14.77/2.81 | | ALPHA: (36) implies: % 14.77/2.81 | | (37) ! [v0: any] : ( ~ (aSet0(all_17_0) = v0) | ~ $i(all_17_0) | (v0 = % 14.77/2.81 | | 0 & ! [v1: $i] : ! [v2: any] : ( ~ (aElement0(v1) = v2) | ~ % 14.77/2.81 | | $i(v1) | ? [v3: any] : ? [v4: any] : (aElementOf0(v1, % 14.77/2.81 | | all_17_0) = v3 & aElementOf0(v1, all_17_1) = v4 & ( ~ (v3 % 14.77/2.81 | | = 0) | (v4 = 0 & v2 = 0 & ~ (v1 = xx))))) & ! [v1: $i] % 14.77/2.81 | | : (v1 = xx | ~ (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : % 14.77/2.81 | | ? [v3: any] : (aElementOf0(v1, all_17_0) = v3 & % 14.77/2.81 | | aElementOf0(v1, all_17_1) = v2 & ( ~ (v2 = 0) | v3 = 0))))) % 14.77/2.81 | | (38) ! [v0: any] : (v0 = all_17_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? % 14.77/2.81 | | [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] : % 14.77/2.81 | | (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1, % 14.77/2.81 | | all_17_1) = v4 & $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 % 14.77/2.81 | | = 0) | v1 = xx) & (v2 = 0 | (v4 = 0 & v3 = 0 & ~ (v1 = % 14.77/2.81 | | xx))))) % 14.77/2.81 | | % 14.77/2.81 | | GROUND_INST: instantiating (38) with xS, simplifying with (2), (5) gives: % 14.77/2.81 | | (39) all_17_0 = xS | ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: % 14.77/2.81 | | any] : (aElement0(v0) = v2 & aElementOf0(v0, all_17_1) = v3 & % 14.77/2.81 | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0) | % 14.77/2.81 | | ~ (v1 = 0) | v0 = xx) & (v1 = 0 | (v3 = 0 & v2 = 0 & ~ (v0 = % 14.77/2.81 | | xx)))) % 14.77/2.81 | | % 14.77/2.81 | | GROUND_INST: instantiating (37) with 0, simplifying with (16), (18) gives: % 14.77/2.82 | | (40) ! [v0: $i] : ! [v1: any] : ( ~ (aElement0(v0) = v1) | ~ $i(v0) | % 14.77/2.82 | | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_17_0) = v2 & % 14.77/2.82 | | aElementOf0(v0, all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 % 14.77/2.82 | | & ~ (v0 = xx))))) & ! [v0: $i] : (v0 = xx | ~ % 14.77/2.82 | | (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 14.77/2.82 | | (aElementOf0(v0, all_17_0) = v2 & aElementOf0(v0, all_17_1) = v1 & % 14.77/2.82 | | ( ~ (v1 = 0) | v2 = 0))) % 14.77/2.82 | | % 14.77/2.82 | | ALPHA: (40) implies: % 14.77/2.82 | | (41) ! [v0: $i] : ! [v1: any] : ( ~ (aElement0(v0) = v1) | ~ $i(v0) | % 14.77/2.82 | | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_17_0) = v2 & % 14.77/2.82 | | aElementOf0(v0, all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 % 14.77/2.82 | | & ~ (v0 = xx))))) % 14.77/2.82 | | % 14.77/2.82 | | BETA: splitting (23) gives: % 14.77/2.82 | | % 14.77/2.82 | | Case 1: % 14.77/2.82 | | | % 14.77/2.82 | | | (42) ? [v0: any] : ? [v1: any] : (aSet0(xS) = v0 & aElement0(xx) = v1 % 14.77/2.82 | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.77/2.82 | | | % 14.77/2.82 | | | DELTA: instantiating (42) with fresh symbols all_41_0, all_41_1 gives: % 14.77/2.82 | | | (43) aSet0(xS) = all_41_1 & aElement0(xx) = all_41_0 & ( ~ (all_41_0 = % 14.77/2.82 | | | 0) | ~ (all_41_1 = 0)) % 14.77/2.82 | | | % 14.77/2.82 | | | ALPHA: (43) implies: % 14.77/2.82 | | | (44) aElement0(xx) = all_41_0 % 14.77/2.82 | | | (45) aSet0(xS) = all_41_1 % 14.77/2.82 | | | (46) ~ (all_41_0 = 0) | ~ (all_41_1 = 0) % 14.77/2.82 | | | % 14.77/2.82 | | | GROUND_INST: instantiating (7) with 0, all_41_0, xx, simplifying with (1), % 14.77/2.82 | | | (44) gives: % 14.77/2.82 | | | (47) all_41_0 = 0 % 14.77/2.82 | | | % 14.77/2.82 | | | GROUND_INST: instantiating (8) with 0, all_41_1, xS, simplifying with (2), % 14.77/2.82 | | | (45) gives: % 14.77/2.82 | | | (48) all_41_1 = 0 % 14.77/2.82 | | | % 14.77/2.82 | | | BETA: splitting (46) gives: % 14.77/2.82 | | | % 14.77/2.82 | | | Case 1: % 14.77/2.82 | | | | % 14.77/2.82 | | | | (49) ~ (all_41_0 = 0) % 14.77/2.82 | | | | % 14.77/2.82 | | | | REDUCE: (47), (49) imply: % 14.77/2.82 | | | | (50) $false % 14.77/2.82 | | | | % 14.77/2.82 | | | | CLOSE: (50) is inconsistent. % 14.77/2.82 | | | | % 14.77/2.82 | | | Case 2: % 14.77/2.82 | | | | % 14.77/2.82 | | | | (51) ~ (all_41_1 = 0) % 14.77/2.82 | | | | % 14.77/2.82 | | | | REDUCE: (48), (51) imply: % 14.77/2.82 | | | | (52) $false % 14.77/2.82 | | | | % 14.77/2.82 | | | | CLOSE: (52) is inconsistent. % 14.77/2.82 | | | | % 14.77/2.82 | | | End of split % 14.77/2.82 | | | % 14.77/2.82 | | Case 2: % 14.77/2.82 | | | % 14.77/2.82 | | | (53) ! [v0: any] : (v0 = all_17_1 | ~ (aSet0(v0) = 0) | ~ $i(v0) | % 14.77/2.82 | | | ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] : % 14.77/2.82 | | | (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1, % 14.77/2.82 | | | xS) = v4 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0) | ( ~ (v4 = % 14.77/2.82 | | | 0) & ~ (v1 = xx))) & (v2 = 0 | (v3 = 0 & (v4 = 0 | v1 = % 14.77/2.82 | | | xx))))) & ! [v0: any] : ( ~ (aSet0(all_17_1) = v0) | ~ % 14.77/2.82 | | | $i(all_17_1) | (v0 = 0 & ! [v1: $i] : ! [v2: any] : ( ~ % 14.77/2.82 | | | (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 14.77/2.82 | | | any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1, % 14.77/2.82 | | | xS) = v4 & ( ~ (v3 = 0) | (v2 = 0 & (v4 = 0 | v1 = % 14.77/2.82 | | | xx))))) & ! [v1: $i] : ( ~ (aElement0(v1) = 0) | ~ % 14.77/2.82 | | | $i(v1) | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, % 14.77/2.82 | | | all_17_1) = v3 & aElementOf0(v1, xS) = v2 & (v3 = 0 | ( % 14.77/2.82 | | | ~ (v2 = 0) & ~ (v1 = xx))))))) % 14.77/2.82 | | | % 14.77/2.82 | | | ALPHA: (53) implies: % 14.77/2.82 | | | (54) ! [v0: any] : ( ~ (aSet0(all_17_1) = v0) | ~ $i(all_17_1) | (v0 % 14.77/2.82 | | | = 0 & ! [v1: $i] : ! [v2: any] : ( ~ (aElement0(v1) = v2) | % 14.77/2.82 | | | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (aElementOf0(v1, % 14.77/2.82 | | | all_17_1) = v3 & aElementOf0(v1, xS) = v4 & ( ~ (v3 = 0) % 14.77/2.82 | | | | (v2 = 0 & (v4 = 0 | v1 = xx))))) & ! [v1: $i] : ( ~ % 14.77/2.82 | | | (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 14.77/2.82 | | | any] : (aElementOf0(v1, all_17_1) = v3 & aElementOf0(v1, % 14.77/2.82 | | | xS) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = xx))))))) % 14.77/2.82 | | | % 14.77/2.82 | | | GROUND_INST: instantiating (54) with 0, simplifying with (15), (17) gives: % 14.77/2.83 | | | (55) ! [v0: $i] : ! [v1: any] : ( ~ (aElement0(v0) = v1) | ~ $i(v0) % 14.77/2.83 | | | | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_17_1) = v2 % 14.77/2.83 | | | & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | (v1 = 0 & (v3 = 0 % 14.77/2.83 | | | | v0 = xx))))) & ! [v0: $i] : ( ~ (aElement0(v0) = 0) | % 14.77/2.83 | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (aElementOf0(v0, % 14.77/2.83 | | | all_17_1) = v2 & aElementOf0(v0, xS) = v1 & (v2 = 0 | ( ~ % 14.77/2.83 | | | (v1 = 0) & ~ (v0 = xx))))) % 14.77/2.83 | | | % 14.77/2.83 | | | ALPHA: (55) implies: % 14.77/2.83 | | | (56) ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: any] : % 14.77/2.83 | | | ? [v2: any] : (aElementOf0(v0, all_17_1) = v2 & aElementOf0(v0, % 14.77/2.83 | | | xS) = v1 & (v2 = 0 | ( ~ (v1 = 0) & ~ (v0 = xx))))) % 14.77/2.83 | | | (57) ! [v0: $i] : ! [v1: any] : ( ~ (aElement0(v0) = v1) | ~ $i(v0) % 14.77/2.83 | | | | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_17_1) = v2 % 14.77/2.83 | | | & aElementOf0(v0, xS) = v3 & ( ~ (v2 = 0) | (v1 = 0 & (v3 = 0 % 14.77/2.83 | | | | v0 = xx))))) % 14.77/2.83 | | | % 14.77/2.83 | | | GROUND_INST: instantiating (56) with xx, simplifying with (1), (4) gives: % 15.15/2.83 | | | (58) ? [v0: MultipleValueBool] : (aElementOf0(xx, all_17_1) = 0 & % 15.15/2.83 | | | aElementOf0(xx, xS) = v0) % 15.15/2.83 | | | % 15.15/2.83 | | | GROUND_INST: instantiating (57) with xx, 0, simplifying with (1), (4) % 15.15/2.83 | | | gives: % 15.15/2.83 | | | (59) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : % 15.15/2.83 | | | (aElementOf0(xx, all_17_1) = v0 & aElementOf0(xx, xS) = v1) % 15.15/2.83 | | | % 15.15/2.83 | | | DELTA: instantiating (59) with fresh symbols all_43_0, all_43_1 gives: % 15.15/2.83 | | | (60) aElementOf0(xx, all_17_1) = all_43_1 & aElementOf0(xx, xS) = % 15.15/2.83 | | | all_43_0 % 15.15/2.83 | | | % 15.15/2.83 | | | ALPHA: (60) implies: % 15.15/2.83 | | | (61) aElementOf0(xx, xS) = all_43_0 % 15.15/2.83 | | | % 15.15/2.83 | | | DELTA: instantiating (58) with fresh symbol all_45_0 gives: % 15.15/2.83 | | | (62) aElementOf0(xx, all_17_1) = 0 & aElementOf0(xx, xS) = all_45_0 % 15.15/2.83 | | | % 15.15/2.83 | | | ALPHA: (62) implies: % 15.15/2.83 | | | (63) aElementOf0(xx, xS) = all_45_0 % 15.15/2.83 | | | % 15.15/2.83 | | | BETA: splitting (39) gives: % 15.15/2.83 | | | % 15.15/2.83 | | | Case 1: % 15.15/2.83 | | | | % 15.15/2.83 | | | | (64) all_17_0 = xS % 15.15/2.83 | | | | % 15.15/2.83 | | | | REDUCE: (14), (64) imply: % 15.15/2.83 | | | | (65) $false % 15.15/2.83 | | | | % 15.15/2.83 | | | | CLOSE: (65) is inconsistent. % 15.15/2.83 | | | | % 15.15/2.83 | | | Case 2: % 15.15/2.83 | | | | % 15.15/2.83 | | | | (66) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 15.15/2.83 | | | | (aElement0(v0) = v2 & aElementOf0(v0, all_17_1) = v3 & % 15.15/2.83 | | | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0) % 15.15/2.83 | | | | | ~ (v1 = 0) | v0 = xx) & (v1 = 0 | (v3 = 0 & v2 = 0 & ~ % 15.15/2.83 | | | | (v0 = xx)))) % 15.15/2.83 | | | | % 15.15/2.83 | | | | DELTA: instantiating (66) with fresh symbols all_51_0, all_51_1, % 15.15/2.83 | | | | all_51_2, all_51_3 gives: % 15.15/2.83 | | | | (67) aElement0(all_51_3) = all_51_1 & aElementOf0(all_51_3, all_17_1) % 15.15/2.83 | | | | = all_51_0 & aElementOf0(all_51_3, xS) = all_51_2 & $i(all_51_3) % 15.15/2.83 | | | | & ( ~ (all_51_0 = 0) | ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | % 15.15/2.83 | | | | all_51_3 = xx) & (all_51_2 = 0 | (all_51_0 = 0 & all_51_1 = 0 % 15.15/2.83 | | | | & ~ (all_51_3 = xx))) % 15.15/2.83 | | | | % 15.15/2.83 | | | | ALPHA: (67) implies: % 15.15/2.83 | | | | (68) $i(all_51_3) % 15.15/2.83 | | | | (69) aElementOf0(all_51_3, xS) = all_51_2 % 15.15/2.83 | | | | (70) aElementOf0(all_51_3, all_17_1) = all_51_0 % 15.15/2.83 | | | | (71) aElement0(all_51_3) = all_51_1 % 15.15/2.83 | | | | (72) all_51_2 = 0 | (all_51_0 = 0 & all_51_1 = 0 & ~ (all_51_3 = % 15.15/2.83 | | | | xx)) % 15.15/2.83 | | | | (73) ~ (all_51_0 = 0) | ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | % 15.15/2.83 | | | | all_51_3 = xx % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (9) with all_15_0, all_45_0, xS, xx, % 15.15/2.83 | | | | simplifying with (12), (63) gives: % 15.15/2.83 | | | | (74) all_45_0 = all_15_0 % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (9) with all_43_0, all_45_0, xS, xx, % 15.15/2.83 | | | | simplifying with (61), (63) gives: % 15.15/2.83 | | | | (75) all_45_0 = all_43_0 % 15.15/2.83 | | | | % 15.15/2.83 | | | | COMBINE_EQS: (74), (75) imply: % 15.15/2.83 | | | | (76) all_43_0 = all_15_0 % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (21) with all_51_3, all_51_0, simplifying % 15.15/2.83 | | | | with (68), (70) gives: % 15.15/2.83 | | | | (77) all_51_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.15/2.83 | | | | (aElement0(all_51_3) = v0 & aElementOf0(all_51_3, xS) = v1 & ( ~ % 15.15/2.83 | | | | (v0 = 0) | ( ~ (v1 = 0) & ~ (all_51_3 = xx)))) % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (22) with all_51_3, all_51_1, simplifying % 15.15/2.83 | | | | with (68), (71) gives: % 15.15/2.83 | | | | (78) all_51_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 15.15/2.83 | | | | aElementOf0(all_51_3, xS) = v0) % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (41) with all_51_3, all_51_1, simplifying % 15.15/2.83 | | | | with (68), (71) gives: % 15.15/2.83 | | | | (79) ? [v0: any] : ? [v1: any] : (aElementOf0(all_51_3, all_17_0) = % 15.15/2.83 | | | | v0 & aElementOf0(all_51_3, all_17_1) = v1 & ( ~ (v0 = 0) | (v1 % 15.15/2.83 | | | | = 0 & all_51_1 = 0 & ~ (all_51_3 = xx)))) % 15.15/2.83 | | | | % 15.15/2.83 | | | | GROUND_INST: instantiating (57) with all_51_3, all_51_1, simplifying % 15.15/2.83 | | | | with (68), (71) gives: % 15.15/2.84 | | | | (80) ? [v0: any] : ? [v1: any] : (aElementOf0(all_51_3, all_17_1) = % 15.15/2.84 | | | | v0 & aElementOf0(all_51_3, xS) = v1 & ( ~ (v0 = 0) | (all_51_1 % 15.15/2.84 | | | | = 0 & (v1 = 0 | all_51_3 = xx)))) % 15.15/2.84 | | | | % 15.15/2.84 | | | | DELTA: instantiating (80) with fresh symbols all_62_0, all_62_1 gives: % 15.15/2.84 | | | | (81) aElementOf0(all_51_3, all_17_1) = all_62_1 & % 15.15/2.84 | | | | aElementOf0(all_51_3, xS) = all_62_0 & ( ~ (all_62_1 = 0) | % 15.15/2.84 | | | | (all_51_1 = 0 & (all_62_0 = 0 | all_51_3 = xx))) % 15.15/2.84 | | | | % 15.15/2.84 | | | | ALPHA: (81) implies: % 15.15/2.84 | | | | (82) aElementOf0(all_51_3, xS) = all_62_0 % 15.15/2.84 | | | | (83) aElementOf0(all_51_3, all_17_1) = all_62_1 % 15.15/2.84 | | | | (84) ~ (all_62_1 = 0) | (all_51_1 = 0 & (all_62_0 = 0 | all_51_3 = % 15.15/2.84 | | | | xx)) % 15.15/2.84 | | | | % 15.15/2.84 | | | | DELTA: instantiating (79) with fresh symbols all_64_0, all_64_1 gives: % 15.15/2.84 | | | | (85) aElementOf0(all_51_3, all_17_0) = all_64_1 & % 15.15/2.84 | | | | aElementOf0(all_51_3, all_17_1) = all_64_0 & ( ~ (all_64_1 = 0) % 15.15/2.84 | | | | | (all_64_0 = 0 & all_51_1 = 0 & ~ (all_51_3 = xx))) % 15.15/2.84 | | | | % 15.15/2.84 | | | | ALPHA: (85) implies: % 15.15/2.84 | | | | (86) aElementOf0(all_51_3, all_17_1) = all_64_0 % 15.15/2.84 | | | | % 15.15/2.84 | | | | GROUND_INST: instantiating (9) with all_51_2, all_62_0, xS, all_51_3, % 15.15/2.84 | | | | simplifying with (69), (82) gives: % 15.15/2.84 | | | | (87) all_62_0 = all_51_2 % 15.15/2.84 | | | | % 15.15/2.84 | | | | GROUND_INST: instantiating (9) with all_51_0, all_64_0, all_17_1, % 15.15/2.84 | | | | all_51_3, simplifying with (70), (86) gives: % 15.15/2.84 | | | | (88) all_64_0 = all_51_0 % 15.15/2.84 | | | | % 15.15/2.84 | | | | GROUND_INST: instantiating (9) with all_62_1, all_64_0, all_17_1, % 15.15/2.84 | | | | all_51_3, simplifying with (83), (86) gives: % 15.15/2.84 | | | | (89) all_64_0 = all_62_1 % 15.15/2.84 | | | | % 15.15/2.84 | | | | COMBINE_EQS: (88), (89) imply: % 15.15/2.84 | | | | (90) all_62_1 = all_51_0 % 15.15/2.84 | | | | % 15.15/2.84 | | | | BETA: splitting (72) gives: % 15.15/2.84 | | | | % 15.15/2.84 | | | | Case 1: % 15.15/2.84 | | | | | % 15.15/2.84 | | | | | (91) all_51_2 = 0 % 15.15/2.84 | | | | | % 15.15/2.84 | | | | | REDUCE: (69), (91) imply: % 15.15/2.84 | | | | | (92) aElementOf0(all_51_3, xS) = 0 % 15.15/2.84 | | | | | % 15.15/2.84 | | | | | BETA: splitting (78) gives: % 15.15/2.84 | | | | | % 15.15/2.84 | | | | | Case 1: % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | (93) all_51_1 = 0 % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | REDUCE: (71), (93) imply: % 15.15/2.84 | | | | | | (94) aElement0(all_51_3) = 0 % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | BETA: splitting (77) gives: % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | Case 1: % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | (95) all_51_0 = 0 % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | BETA: splitting (73) gives: % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | Case 1: % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | (96) ~ (all_51_0 = 0) % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | REDUCE: (95), (96) imply: % 15.15/2.84 | | | | | | | | (97) $false % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | CLOSE: (97) is inconsistent. % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | Case 2: % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | (98) ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | all_51_3 = xx % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | BETA: splitting (98) gives: % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | Case 1: % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | (99) ~ (all_51_1 = 0) % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | REDUCE: (93), (99) imply: % 15.15/2.84 | | | | | | | | | (100) $false % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | CLOSE: (100) is inconsistent. % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | Case 2: % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | (101) ~ (all_51_2 = 0) | all_51_3 = xx % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | BETA: splitting (101) gives: % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | | Case 1: % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | (102) ~ (all_51_2 = 0) % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | REDUCE: (91), (102) imply: % 15.15/2.84 | | | | | | | | | | (103) $false % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | CLOSE: (103) is inconsistent. % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | Case 2: % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | (104) all_51_3 = xx % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | REDUCE: (92), (104) imply: % 15.15/2.84 | | | | | | | | | | (105) aElementOf0(xx, xS) = 0 % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | GROUND_INST: instantiating (9) with all_15_0, 0, xS, xx, % 15.15/2.84 | | | | | | | | | | simplifying with (12), (105) gives: % 15.15/2.84 | | | | | | | | | | (106) all_15_0 = 0 % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | REDUCE: (11), (106) imply: % 15.15/2.84 | | | | | | | | | | (107) $false % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | | CLOSE: (107) is inconsistent. % 15.15/2.84 | | | | | | | | | | % 15.15/2.84 | | | | | | | | | End of split % 15.15/2.84 | | | | | | | | | % 15.15/2.84 | | | | | | | | End of split % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | End of split % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | Case 2: % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | (108) ? [v0: any] : ? [v1: any] : (aElement0(all_51_3) = v0 & % 15.15/2.84 | | | | | | | aElementOf0(all_51_3, xS) = v1 & ( ~ (v0 = 0) | ( ~ (v1 % 15.15/2.84 | | | | | | | = 0) & ~ (all_51_3 = xx)))) % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | DELTA: instantiating (108) with fresh symbols all_231_0, all_231_1 % 15.15/2.84 | | | | | | | gives: % 15.15/2.84 | | | | | | | (109) aElement0(all_51_3) = all_231_1 & aElementOf0(all_51_3, % 15.15/2.84 | | | | | | | xS) = all_231_0 & ( ~ (all_231_1 = 0) | ( ~ (all_231_0 % 15.15/2.84 | | | | | | | = 0) & ~ (all_51_3 = xx))) % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | ALPHA: (109) implies: % 15.15/2.84 | | | | | | | (110) aElementOf0(all_51_3, xS) = all_231_0 % 15.15/2.84 | | | | | | | (111) aElement0(all_51_3) = all_231_1 % 15.15/2.84 | | | | | | | (112) ~ (all_231_1 = 0) | ( ~ (all_231_0 = 0) & ~ (all_51_3 = % 15.15/2.84 | | | | | | | xx)) % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | GROUND_INST: instantiating (9) with 0, all_231_0, xS, all_51_3, % 15.15/2.84 | | | | | | | simplifying with (92), (110) gives: % 15.15/2.84 | | | | | | | (113) all_231_0 = 0 % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | GROUND_INST: instantiating (7) with 0, all_231_1, all_51_3, % 15.15/2.84 | | | | | | | simplifying with (94), (111) gives: % 15.15/2.84 | | | | | | | (114) all_231_1 = 0 % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | BETA: splitting (112) gives: % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | | Case 1: % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | (115) ~ (all_231_1 = 0) % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | REDUCE: (114), (115) imply: % 15.15/2.84 | | | | | | | | (116) $false % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | CLOSE: (116) is inconsistent. % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | Case 2: % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | (117) ~ (all_231_0 = 0) & ~ (all_51_3 = xx) % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | ALPHA: (117) implies: % 15.15/2.84 | | | | | | | | (118) ~ (all_231_0 = 0) % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | REDUCE: (113), (118) imply: % 15.15/2.84 | | | | | | | | (119) $false % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | | CLOSE: (119) is inconsistent. % 15.15/2.84 | | | | | | | | % 15.15/2.84 | | | | | | | End of split % 15.15/2.84 | | | | | | | % 15.15/2.84 | | | | | | End of split % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | Case 2: % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | (120) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_51_3, xS) = % 15.15/2.84 | | | | | | v0) % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | DELTA: instantiating (120) with fresh symbol all_227_0 gives: % 15.15/2.84 | | | | | | (121) ~ (all_227_0 = 0) & aElementOf0(all_51_3, xS) = all_227_0 % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | ALPHA: (121) implies: % 15.15/2.84 | | | | | | (122) ~ (all_227_0 = 0) % 15.15/2.84 | | | | | | (123) aElementOf0(all_51_3, xS) = all_227_0 % 15.15/2.84 | | | | | | % 15.15/2.84 | | | | | | GROUND_INST: instantiating (9) with 0, all_227_0, xS, all_51_3, % 15.15/2.84 | | | | | | simplifying with (92), (123) gives: % 15.15/2.84 | | | | | | (124) all_227_0 = 0 % 15.15/2.84 | | | | | | % 15.15/2.85 | | | | | | REDUCE: (122), (124) imply: % 15.15/2.85 | | | | | | (125) $false % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | CLOSE: (125) is inconsistent. % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | End of split % 15.15/2.85 | | | | | % 15.15/2.85 | | | | Case 2: % 15.15/2.85 | | | | | % 15.15/2.85 | | | | | (126) ~ (all_51_2 = 0) % 15.15/2.85 | | | | | (127) all_51_0 = 0 & all_51_1 = 0 & ~ (all_51_3 = xx) % 15.15/2.85 | | | | | % 15.15/2.85 | | | | | ALPHA: (127) implies: % 15.15/2.85 | | | | | (128) all_51_0 = 0 % 15.15/2.85 | | | | | (129) ~ (all_51_3 = xx) % 15.15/2.85 | | | | | % 15.15/2.85 | | | | | COMBINE_EQS: (90), (128) imply: % 15.15/2.85 | | | | | (130) all_62_1 = 0 % 15.15/2.85 | | | | | % 15.15/2.85 | | | | | BETA: splitting (84) gives: % 15.15/2.85 | | | | | % 15.15/2.85 | | | | | Case 1: % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | (131) ~ (all_62_1 = 0) % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | REDUCE: (130), (131) imply: % 15.15/2.85 | | | | | | (132) $false % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | CLOSE: (132) is inconsistent. % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | Case 2: % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | (133) all_51_1 = 0 & (all_62_0 = 0 | all_51_3 = xx) % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | ALPHA: (133) implies: % 15.15/2.85 | | | | | | (134) all_62_0 = 0 | all_51_3 = xx % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | BETA: splitting (134) gives: % 15.15/2.85 | | | | | | % 15.15/2.85 | | | | | | Case 1: % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | (135) all_51_3 = xx % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | REDUCE: (129), (135) imply: % 15.15/2.85 | | | | | | | (136) $false % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | CLOSE: (136) is inconsistent. % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | Case 2: % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | (137) all_62_0 = 0 % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | COMBINE_EQS: (87), (137) imply: % 15.15/2.85 | | | | | | | (138) all_51_2 = 0 % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | SIMP: (138) implies: % 15.15/2.85 | | | | | | | (139) all_51_2 = 0 % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | REDUCE: (126), (139) imply: % 15.15/2.85 | | | | | | | (140) $false % 15.15/2.85 | | | | | | | % 15.15/2.85 | | | | | | | CLOSE: (140) is inconsistent. % 15.15/2.85 | | | | | | | % 15.64/2.85 | | | | | | End of split % 15.64/2.85 | | | | | | % 15.64/2.85 | | | | | End of split % 15.64/2.85 | | | | | % 15.64/2.85 | | | | End of split % 15.64/2.85 | | | | % 15.64/2.85 | | | End of split % 15.64/2.85 | | | % 15.64/2.85 | | End of split % 15.64/2.85 | | % 15.64/2.85 | End of split % 15.64/2.85 | % 15.64/2.85 End of proof % 15.64/2.85 % SZS output end Proof for theBenchmark % 15.64/2.85 % 15.64/2.85 2237ms %------------------------------------------------------------------------------