%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM535+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 : n018.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 20.94s 3.75s % Output : Proof 22.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM535+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 13:44:28 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.55/1.08 Prover 4: Preprocessing ... % 2.55/1.08 Prover 1: Preprocessing ... % 2.55/1.12 Prover 0: Preprocessing ... % 2.55/1.12 Prover 5: Preprocessing ... % 2.55/1.12 Prover 3: Preprocessing ... % 3.20/1.12 Prover 6: Preprocessing ... % 3.20/1.13 Prover 2: Preprocessing ... % 7.22/1.79 Prover 1: Constructing countermodel ... % 7.22/1.79 Prover 5: Constructing countermodel ... % 7.80/1.80 Prover 2: Proving ... % 7.80/1.80 Prover 3: Constructing countermodel ... % 7.80/1.82 Prover 6: Proving ... % 9.36/2.07 Prover 4: Constructing countermodel ... % 10.58/2.24 Prover 0: Proving ... % 20.94/3.74 Prover 1: Found proof (size 113) % 20.94/3.74 Prover 1: proved (3127ms) % 20.94/3.74 Prover 5: stopped % 20.94/3.74 Prover 4: stopped % 20.94/3.74 Prover 0: stopped % 20.94/3.74 Prover 6: stopped % 20.94/3.75 Prover 3: stopped % 20.94/3.75 Prover 2: stopped % 20.94/3.75 % 20.94/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.94/3.75 % 20.94/3.77 % SZS output start Proof for theBenchmark % 20.94/3.77 Assumptions after simplification: % 20.94/3.77 --------------------------------- % 20.94/3.77 % 20.94/3.77 (mDefDiff) % 20.94/3.82 ! [v0: $i] : ! [v1: $i] : ( ~ (aSet0(v0) = 0) | ~ (aElement0(v1) = 0) | ~ % 20.94/3.82 $i(v1) | ~ $i(v0) | ? [v2: $i] : (sdtmndt0(v0, v1) = v2 & $i(v2) & ! [v3: % 20.94/3.82 $i] : (v3 = v2 | ~ (aSet0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: % 20.94/3.82 any] : ? [v6: any] : ? [v7: any] : (aElement0(v4) = v6 & % 20.94/3.82 aElementOf0(v4, v3) = v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v7 % 20.94/3.82 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v4 = v1) & (v5 = 0 | (v7 = 0 & % 20.94/3.82 v6 = 0 & ~ (v4 = v1))))) & ! [v3: any] : ( ~ (aSet0(v2) = v3) | % 20.94/3.82 (v3 = 0 & ! [v4: $i] : ! [v5: any] : ( ~ (aElement0(v4) = v5) | ~ % 20.94/3.83 $i(v4) | ? [v6: any] : ? [v7: any] : (aElementOf0(v4, v2) = v6 & % 21.91/3.83 aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v7 = 0 & v5 = 0 & ~ % 21.91/3.83 (v4 = v1))))) & ! [v4: $i] : (v4 = v1 | ~ (aElement0(v4) = % 21.91/3.83 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (aElementOf0(v4, % 21.91/3.83 v2) = v6 & aElementOf0(v4, v0) = v5 & ( ~ (v5 = 0) | v6 = % 21.91/3.83 0))))))) % 21.91/3.83 % 21.91/3.83 (mDefSub) % 21.91/3.83 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] : % 21.91/3.83 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 21.91/3.83 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) = % 21.91/3.83 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & ! % 21.91/3.83 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & ! % 21.91/3.83 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ % 21.91/3.83 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) = % 21.91/3.83 v4)))))) % 21.91/3.83 % 21.91/3.83 (mEOfElem) % 21.91/3.84 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : % 21.91/3.84 (v2 = 0 | ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 21.91/3.84 & aElementOf0(v1, v0) = v3))) % 21.91/3.84 % 21.91/3.84 (m__) % 21.91/3.85 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 21.91/3.85 (sdtmndt0(xS, xx) = v0 & sdtpldt0(v0, xx) = v1 & aSubsetOf0(v1, xS) = v3 & % 21.91/3.85 aSubsetOf0(xS, v1) = v2 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) & $i(v0) & % 21.91/3.85 ! [v4: $i] : ! [v5: int] : (v5 = 0 | v4 = xx | ~ (aElementOf0(v4, v0) = % 21.91/3.85 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (aElement0(v4) = v6 & % 21.91/3.85 aElementOf0(v4, xS) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4: $i] : % 21.91/3.85 ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = v5) | ~ $i(v4) | ? [v6: % 21.91/3.85 any] : ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v0) = v7 & ( % 21.91/3.85 ~ (v6 = 0) | ( ~ (v7 = 0) & ~ (v4 = xx))))) & ! [v4: $i] : ( ~ % 21.91/3.85 (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: any] : (aElement0(v4) = 0 % 21.91/3.85 & aElementOf0(v4, v0) = v5 & (v5 = 0 | v4 = xx))) & ! [v4: $i] : ( ~ % 21.91/3.85 (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ( ~ (v4 = xx) & aElement0(v4) = 0 % 21.91/3.85 & aElementOf0(v4, xS) = 0)) & (( ~ (v3 = 0) & ? [v4: $i] : ? [v5: int] % 21.91/3.85 : ( ~ (v5 = 0) & aElementOf0(v4, v1) = 0 & aElementOf0(v4, xS) = v5 & % 21.91/3.85 $i(v4))) | ( ~ (v2 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 21.91/3.85 aElementOf0(v4, v1) = v5 & aElementOf0(v4, xS) = 0 & $i(v4))))) % 21.91/3.85 % 21.91/3.85 (m__617) % 21.91/3.85 aSet0(xS) = 0 & $i(xS) % 21.91/3.85 % 21.91/3.85 (m__617_02) % 21.91/3.85 aElementOf0(xx, xS) = 0 & $i(xx) & $i(xS) % 21.91/3.85 % 21.91/3.85 (function-axioms) % 21.91/3.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.91/3.86 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 21.91/3.86 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 21.91/3.86 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.91/3.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.91/3.86 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0: % 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.91/3.86 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & % 21.91/3.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 21.91/3.86 v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & ! [v0: % 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.91/3.86 ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.91/3.86 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.91/3.86 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 21.91/3.86 ~ (aElement0(v2) = v0)) % 21.91/3.86 % 21.91/3.86 Further assumptions not needed in the proof: % 21.91/3.86 -------------------------------------------- % 21.91/3.86 mCntRel, mCountNFin, mCountNFin_01, mDefCons, mDefEmp, mElmSort, mEmpFin, % 21.91/3.86 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans % 21.91/3.86 % 21.91/3.86 Those formulas are unsatisfiable: % 21.91/3.86 --------------------------------- % 21.91/3.86 % 21.91/3.86 Begin of proof % 21.91/3.86 | % 21.91/3.86 | ALPHA: (m__617) implies: % 21.91/3.86 | (1) aSet0(xS) = 0 % 21.91/3.86 | % 21.91/3.86 | ALPHA: (m__617_02) implies: % 21.91/3.87 | (2) aElementOf0(xx, xS) = 0 % 21.91/3.87 | % 21.91/3.87 | ALPHA: (m__) implies: % 21.91/3.87 | (3) $i(xS) % 21.91/3.88 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (sdtmndt0(xS, % 21.91/3.88 | xx) = v0 & sdtpldt0(v0, xx) = v1 & aSubsetOf0(v1, xS) = v3 & % 21.91/3.88 | aSubsetOf0(xS, v1) = v2 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) & % 21.91/3.88 | $i(v0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | v4 = xx | ~ % 21.91/3.88 | (aElementOf0(v4, v0) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 21.91/3.88 | any] : (aElement0(v4) = v6 & aElementOf0(v4, xS) = v7 & ( ~ (v7 = % 21.91/3.88 | 0) | ~ (v6 = 0)))) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | % 21.91/3.88 | ~ (aElementOf0(v4, v1) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 21.91/3.88 | any] : (aElement0(v4) = v6 & aElementOf0(v4, v0) = v7 & ( ~ (v6 = % 21.91/3.88 | 0) | ( ~ (v7 = 0) & ~ (v4 = xx))))) & ! [v4: $i] : ( ~ % 21.91/3.88 | (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: any] : % 21.91/3.88 | (aElement0(v4) = 0 & aElementOf0(v4, v0) = v5 & (v5 = 0 | v4 = % 21.91/3.88 | xx))) & ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) % 21.91/3.88 | | ( ~ (v4 = xx) & aElement0(v4) = 0 & aElementOf0(v4, xS) = 0)) & % 21.91/3.88 | (( ~ (v3 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 21.91/3.88 | aElementOf0(v4, v1) = 0 & aElementOf0(v4, xS) = v5 & $i(v4))) | % 21.91/3.88 | ( ~ (v2 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 21.91/3.88 | aElementOf0(v4, v1) = v5 & aElementOf0(v4, xS) = 0 & $i(v4))))) % 21.91/3.88 | % 21.91/3.88 | ALPHA: (function-axioms) implies: % 21.91/3.88 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.91/3.88 | (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 21.91/3.88 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.91/3.88 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 21.91/3.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.91/3.88 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 21.91/3.88 | (aElementOf0(v3, v2) = v0)) % 21.91/3.88 | % 21.91/3.88 | DELTA: instantiating (4) with fresh symbols all_14_0, all_14_1, all_14_2, % 21.91/3.88 | all_14_3 gives: % 21.91/3.89 | (8) sdtmndt0(xS, xx) = all_14_3 & sdtpldt0(all_14_3, xx) = all_14_2 & % 21.91/3.89 | aSubsetOf0(all_14_2, xS) = all_14_0 & aSubsetOf0(xS, all_14_2) = % 21.91/3.89 | all_14_1 & aSet0(all_14_2) = 0 & aSet0(all_14_3) = 0 & $i(all_14_2) & % 21.91/3.89 | $i(all_14_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = xx | ~ % 21.91/3.89 | (aElementOf0(v0, all_14_3) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 21.91/3.89 | any] : (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & ( ~ (v3 = % 21.91/3.89 | 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 21.91/3.89 | (aElementOf0(v0, all_14_2) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 21.91/3.89 | any] : (aElement0(v0) = v2 & aElementOf0(v0, all_14_3) = v3 & ( ~ % 21.91/3.89 | (v2 = 0) | ( ~ (v3 = 0) & ~ (v0 = xx))))) & ! [v0: $i] : ( ~ % 21.91/3.89 | (aElementOf0(v0, all_14_2) = 0) | ~ $i(v0) | ? [v1: any] : % 21.91/3.89 | (aElement0(v0) = 0 & aElementOf0(v0, all_14_3) = v1 & (v1 = 0 | v0 = % 21.91/3.89 | xx))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_3) = 0) | ~ % 21.91/3.89 | $i(v0) | ( ~ (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0, xS) = % 21.91/3.89 | 0)) & (( ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = % 21.91/3.89 | 0) & aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & % 21.91/3.89 | $i(v0))) | ( ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ % 21.91/3.89 | (v1 = 0) & aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = % 21.91/3.89 | 0 & $i(v0)))) % 21.91/3.89 | % 21.91/3.89 | ALPHA: (8) implies: % 21.91/3.89 | (9) $i(all_14_2) % 21.91/3.89 | (10) aSet0(all_14_2) = 0 % 21.91/3.89 | (11) aSubsetOf0(xS, all_14_2) = all_14_1 % 21.91/3.89 | (12) aSubsetOf0(all_14_2, xS) = all_14_0 % 22.51/3.90 | (13) ( ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.51/3.90 | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & % 22.51/3.90 | $i(v0))) | ( ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ % 22.51/3.90 | (v1 = 0) & aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = % 22.51/3.90 | 0 & $i(v0))) % 22.51/3.90 | (14) ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_3) = 0) | ~ $i(v0) | ( ~ % 22.51/3.90 | (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0, xS) = 0)) % 22.51/3.90 | (15) ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_2) = 0) | ~ $i(v0) | ? % 22.51/3.90 | [v1: any] : (aElement0(v0) = 0 & aElementOf0(v0, all_14_3) = v1 & % 22.51/3.90 | (v1 = 0 | v0 = xx))) % 22.51/3.90 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_14_2) = % 22.51/3.90 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) = % 22.51/3.90 | v2 & aElementOf0(v0, all_14_3) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0) % 22.51/3.90 | & ~ (v0 = xx))))) % 22.51/3.90 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = xx | ~ (aElementOf0(v0, % 22.51/3.90 | all_14_3) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 22.51/3.90 | (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & ( ~ (v3 = 0) | ~ % 22.51/3.90 | (v2 = 0)))) % 22.51/3.90 | % 22.51/3.90 | GROUND_INST: instantiating (mEOfElem) with xS, simplifying with (1), (3) % 22.51/3.90 | gives: % 22.51/3.90 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElement0(v0) = v1) | ~ % 22.51/3.90 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xS) = v2)) % 22.51/3.90 | % 22.51/3.90 | GROUND_INST: instantiating (mDefSub) with xS, simplifying with (1), (3) gives: % 22.51/3.91 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xS) = v1) | % 22.51/3.91 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.51/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xS) = v3 & $i(v2)) | ? % 22.51/3.91 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 22.51/3.91 | (aSubsetOf0(v0, xS) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] % 22.51/3.91 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xS) = v2) | ~ % 22.51/3.91 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) = % 22.51/3.91 | v3)))) % 22.51/3.91 | % 22.51/3.91 | ALPHA: (19) implies: % 22.51/3.91 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xS) = v1) | % 22.51/3.91 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.51/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xS) = v3 & $i(v2)) | ? % 22.51/3.91 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) % 22.51/3.91 | % 22.51/3.91 | GROUND_INST: instantiating (mDefSub) with all_14_2, simplifying with (9), (10) % 22.51/3.91 | gives: % 22.58/3.91 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, all_14_2) = % 22.58/3.91 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.58/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, all_14_2) = v3 & $i(v2)) % 22.58/3.91 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 22.58/3.91 | (aSubsetOf0(v0, all_14_2) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! % 22.58/3.91 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, all_14_2) % 22.58/3.91 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 22.58/3.91 | aElementOf0(v1, v0) = v3)))) % 22.58/3.91 | % 22.58/3.91 | ALPHA: (21) implies: % 22.60/3.91 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, all_14_2) = % 22.60/3.91 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.60/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, all_14_2) = v3 & $i(v2)) % 22.60/3.91 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) % 22.60/3.91 | % 22.60/3.91 | GROUND_INST: instantiating (22) with xS, all_14_1, simplifying with (3), (11) % 22.60/3.91 | gives: % 22.60/3.91 | (23) all_14_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.60/3.91 | aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) | % 22.60/3.91 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(xS) = v0) % 22.60/3.91 | % 22.60/3.91 | GROUND_INST: instantiating (20) with all_14_2, all_14_0, simplifying with (9), % 22.60/3.91 | (12) gives: % 22.60/3.91 | (24) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.60/3.91 | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) | % 22.60/3.91 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0) % 22.60/3.91 | % 22.60/3.91 | BETA: splitting (13) gives: % 22.60/3.91 | % 22.60/3.92 | Case 1: % 22.60/3.92 | | % 22.60/3.92 | | (25) ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.60/3.92 | | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) % 22.60/3.92 | | % 22.60/3.92 | | ALPHA: (25) implies: % 22.60/3.92 | | (26) ~ (all_14_0 = 0) % 22.60/3.92 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, % 22.60/3.92 | | all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) % 22.60/3.92 | | % 22.60/3.92 | | DELTA: instantiating (27) with fresh symbols all_40_0, all_40_1 gives: % 22.60/3.92 | | (28) ~ (all_40_0 = 0) & aElementOf0(all_40_1, all_14_2) = 0 & % 22.60/3.92 | | aElementOf0(all_40_1, xS) = all_40_0 & $i(all_40_1) % 22.60/3.92 | | % 22.60/3.92 | | ALPHA: (28) implies: % 22.60/3.92 | | (29) ~ (all_40_0 = 0) % 22.60/3.92 | | (30) $i(all_40_1) % 22.60/3.92 | | (31) aElementOf0(all_40_1, xS) = all_40_0 % 22.60/3.92 | | (32) aElementOf0(all_40_1, all_14_2) = 0 % 22.60/3.92 | | % 22.60/3.92 | | BETA: splitting (24) gives: % 22.60/3.92 | | % 22.60/3.92 | | Case 1: % 22.60/3.92 | | | % 22.60/3.92 | | | (33) all_14_0 = 0 % 22.60/3.92 | | | % 22.60/3.92 | | | REDUCE: (26), (33) imply: % 22.60/3.92 | | | (34) $false % 22.60/3.92 | | | % 22.60/3.92 | | | CLOSE: (34) is inconsistent. % 22.60/3.92 | | | % 22.60/3.92 | | Case 2: % 22.60/3.92 | | | % 22.60/3.92 | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, % 22.60/3.92 | | | all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) | ? [v0: % 22.60/3.92 | | | int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0) % 22.60/3.92 | | | % 22.60/3.92 | | | BETA: splitting (35) gives: % 22.60/3.92 | | | % 22.60/3.92 | | | Case 1: % 22.60/3.92 | | | | % 22.60/3.92 | | | | % 22.60/3.92 | | | | GROUND_INST: instantiating (15) with all_40_1, simplifying with (30), % 22.60/3.92 | | | | (32) gives: % 22.60/3.92 | | | | (36) ? [v0: any] : (aElement0(all_40_1) = 0 & aElementOf0(all_40_1, % 22.60/3.92 | | | | all_14_3) = v0 & (v0 = 0 | all_40_1 = xx)) % 22.60/3.92 | | | | % 22.60/3.92 | | | | DELTA: instantiating (36) with fresh symbol all_58_0 gives: % 22.60/3.92 | | | | (37) aElement0(all_40_1) = 0 & aElementOf0(all_40_1, all_14_3) = % 22.60/3.92 | | | | all_58_0 & (all_58_0 = 0 | all_40_1 = xx) % 22.60/3.92 | | | | % 22.60/3.92 | | | | ALPHA: (37) implies: % 22.60/3.93 | | | | (38) aElementOf0(all_40_1, all_14_3) = all_58_0 % 22.60/3.93 | | | | (39) aElement0(all_40_1) = 0 % 22.60/3.93 | | | | (40) all_58_0 = 0 | all_40_1 = xx % 22.60/3.93 | | | | % 22.60/3.93 | | | | GROUND_INST: instantiating (mDefDiff) with xS, all_40_1, simplifying % 22.60/3.93 | | | | with (1), (3), (30), (39) gives: % 22.60/3.93 | | | | (41) ? [v0: $i] : (sdtmndt0(xS, all_40_1) = v0 & $i(v0) & ! [v1: % 22.60/3.93 | | | | $i] : (v1 = v0 | ~ (aSet0(v1) = 0) | ~ $i(v1) | ? [v2: % 22.60/3.93 | | | | $i] : ? [v3: any] : ? [v4: any] : ? [v5: any] : % 22.60/3.93 | | | | (aElement0(v2) = v4 & aElementOf0(v2, v1) = v3 & % 22.60/3.93 | | | | aElementOf0(v2, xS) = v5 & $i(v2) & ( ~ (v5 = 0) | ~ (v4 % 22.60/3.93 | | | | = 0) | ~ (v3 = 0) | v2 = all_40_1) & (v3 = 0 | (v5 = % 22.60/3.93 | | | | 0 & v4 = 0 & ~ (v2 = all_40_1))))) & ! [v1: any] : ( % 22.60/3.93 | | | | ~ (aSet0(v0) = v1) | (v1 = 0 & ! [v2: $i] : ! [v3: any] : % 22.60/3.93 | | | | ( ~ (aElement0(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 22.60/3.93 | | | | [v5: any] : (aElementOf0(v2, v0) = v4 & aElementOf0(v2, % 22.60/3.93 | | | | xS) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0 & ~ (v2 % 22.60/3.93 | | | | = all_40_1))))) & ! [v2: any] : (v2 = all_40_1 % 22.60/3.93 | | | | | ~ (aElement0(v2) = 0) | ~ $i(v2) | ? [v3: any] : ? % 22.60/3.93 | | | | [v4: any] : (aElementOf0(v2, v0) = v4 & aElementOf0(v2, % 22.60/3.93 | | | | xS) = v3 & ( ~ (v3 = 0) | v4 = 0)))))) % 22.60/3.93 | | | | % 22.60/3.93 | | | | DELTA: instantiating (41) with fresh symbol all_71_0 gives: % 22.60/3.93 | | | | (42) sdtmndt0(xS, all_40_1) = all_71_0 & $i(all_71_0) & ! [v0: any] % 22.60/3.94 | | | | : (v0 = all_71_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 22.60/3.94 | | | | : ? [v2: any] : ? [v3: any] : ? [v4: any] : (aElement0(v1) % 22.60/3.94 | | | | = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1, xS) = v4 & % 22.60/3.94 | | | | $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = % 22.60/3.94 | | | | all_40_1) & (v2 = 0 | (v4 = 0 & v3 = 0 & ~ (v1 = % 22.60/3.94 | | | | all_40_1))))) & ! [v0: any] : ( ~ (aSet0(all_71_0) = % 22.60/3.94 | | | | v0) | (v0 = 0 & ! [v1: $i] : ! [v2: any] : ( ~ % 22.60/3.94 | | | | (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 22.60/3.94 | | | | any] : (aElementOf0(v1, all_71_0) = v3 & aElementOf0(v1, % 22.60/3.94 | | | | xS) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0 & ~ (v1 = % 22.60/3.94 | | | | all_40_1))))) & ! [v1: any] : (v1 = all_40_1 | ~ % 22.60/3.94 | | | | (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 22.60/3.94 | | | | any] : (aElementOf0(v1, all_71_0) = v3 & aElementOf0(v1, % 22.60/3.94 | | | | xS) = v2 & ( ~ (v2 = 0) | v3 = 0))))) % 22.60/3.94 | | | | % 22.60/3.94 | | | | ALPHA: (42) implies: % 22.60/3.94 | | | | (43) ! [v0: any] : (v0 = all_71_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) | % 22.60/3.94 | | | | ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] : % 22.60/3.94 | | | | (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 & % 22.60/3.94 | | | | aElementOf0(v1, xS) = v4 & $i(v1) & ( ~ (v4 = 0) | ~ (v3 = % 22.60/3.94 | | | | 0) | ~ (v2 = 0) | v1 = all_40_1) & (v2 = 0 | (v4 = 0 & % 22.60/3.94 | | | | v3 = 0 & ~ (v1 = all_40_1))))) % 22.60/3.94 | | | | % 22.60/3.94 | | | | GROUND_INST: instantiating (43) with xS, simplifying with (1), (3) % 22.60/3.94 | | | | gives: % 22.60/3.94 | | | | (44) all_71_0 = xS | ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? % 22.60/3.94 | | | | [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & % 22.60/3.94 | | | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0) % 22.60/3.94 | | | | | ~ (v1 = 0) | v0 = all_40_1) & (v1 = 0 | (v3 = 0 & v2 = 0 % 22.60/3.94 | | | | & ~ (v0 = all_40_1)))) % 22.60/3.94 | | | | % 22.60/3.94 | | | | BETA: splitting (40) gives: % 22.60/3.94 | | | | % 22.60/3.94 | | | | Case 1: % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | (45) all_40_1 = xx % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | REDUCE: (31), (45) imply: % 22.60/3.94 | | | | | (46) aElementOf0(xx, xS) = all_40_0 % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | GROUND_INST: instantiating (7) with 0, all_40_0, xS, xx, simplifying % 22.60/3.94 | | | | | with (2), (46) gives: % 22.60/3.94 | | | | | (47) all_40_0 = 0 % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | REDUCE: (29), (47) imply: % 22.60/3.94 | | | | | (48) $false % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | CLOSE: (48) is inconsistent. % 22.60/3.94 | | | | | % 22.60/3.94 | | | | Case 2: % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | (49) all_58_0 = 0 % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | REDUCE: (38), (49) imply: % 22.60/3.94 | | | | | (50) aElementOf0(all_40_1, all_14_3) = 0 % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | BETA: splitting (44) gives: % 22.60/3.94 | | | | | % 22.60/3.94 | | | | | Case 1: % 22.60/3.94 | | | | | | % 22.60/3.94 | | | | | | % 22.60/3.94 | | | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with % 22.60/3.94 | | | | | | (30), (50) gives: % 22.60/3.94 | | | | | | (51) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 & % 22.60/3.94 | | | | | | aElementOf0(all_40_1, xS) = 0 % 22.60/3.94 | | | | | | % 22.60/3.94 | | | | | | REF_CLOSE: (7), (29), (31), (51) are inconsistent by sub-proof #1. % 22.60/3.94 | | | | | | % 22.60/3.94 | | | | | Case 2: % 22.60/3.94 | | | | | | % 22.60/3.95 | | | | | | (52) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.60/3.95 | | | | | | (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & % 22.60/3.95 | | | | | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 % 22.60/3.95 | | | | | | = 0) | ~ (v1 = 0) | v0 = all_40_1) & (v1 = 0 | (v3 = % 22.60/3.95 | | | | | | 0 & v2 = 0 & ~ (v0 = all_40_1)))) % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | | DELTA: instantiating (52) with fresh symbols all_310_0, all_310_1, % 22.60/3.95 | | | | | | all_310_2, all_310_3 gives: % 22.60/3.95 | | | | | | (53) aElement0(all_310_3) = all_310_1 & aElementOf0(all_310_3, % 22.60/3.95 | | | | | | xS) = all_310_0 & aElementOf0(all_310_3, xS) = all_310_2 & % 22.60/3.95 | | | | | | $i(all_310_3) & ( ~ (all_310_0 = 0) | ~ (all_310_1 = 0) | % 22.60/3.95 | | | | | | ~ (all_310_2 = 0) | all_310_3 = all_40_1) & (all_310_2 = 0 % 22.60/3.95 | | | | | | | (all_310_0 = 0 & all_310_1 = 0 & ~ (all_310_3 = % 22.60/3.95 | | | | | | all_40_1))) % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | | ALPHA: (53) implies: % 22.60/3.95 | | | | | | (54) aElementOf0(all_310_3, xS) = all_310_2 % 22.60/3.95 | | | | | | (55) aElementOf0(all_310_3, xS) = all_310_0 % 22.60/3.95 | | | | | | (56) all_310_2 = 0 | (all_310_0 = 0 & all_310_1 = 0 & ~ % 22.60/3.95 | | | | | | (all_310_3 = all_40_1)) % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | | GROUND_INST: instantiating (7) with all_310_2, all_310_0, xS, % 22.60/3.95 | | | | | | all_310_3, simplifying with (54), (55) gives: % 22.60/3.95 | | | | | | (57) all_310_0 = all_310_2 % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | | BETA: splitting (56) gives: % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | | Case 1: % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with % 22.60/3.95 | | | | | | | (30), (50) gives: % 22.60/3.95 | | | | | | | (58) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 & % 22.60/3.95 | | | | | | | aElementOf0(all_40_1, xS) = 0 % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | REF_CLOSE: (7), (29), (31), (58) are inconsistent by sub-proof #1. % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | Case 2: % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | (59) ~ (all_310_2 = 0) % 22.60/3.95 | | | | | | | (60) all_310_0 = 0 & all_310_1 = 0 & ~ (all_310_3 = all_40_1) % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | ALPHA: (60) implies: % 22.60/3.95 | | | | | | | (61) all_310_0 = 0 % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | COMBINE_EQS: (57), (61) imply: % 22.60/3.95 | | | | | | | (62) all_310_2 = 0 % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | REDUCE: (59), (62) imply: % 22.60/3.95 | | | | | | | (63) $false % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | | CLOSE: (63) is inconsistent. % 22.60/3.95 | | | | | | | % 22.60/3.95 | | | | | | End of split % 22.60/3.95 | | | | | | % 22.60/3.95 | | | | | End of split % 22.60/3.95 | | | | | % 22.60/3.95 | | | | End of split % 22.60/3.95 | | | | % 22.60/3.95 | | | Case 2: % 22.60/3.95 | | | | % 22.60/3.95 | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0) % 22.60/3.95 | | | | % 22.60/3.95 | | | | DELTA: instantiating (64) with fresh symbol all_49_0 gives: % 22.60/3.95 | | | | (65) ~ (all_49_0 = 0) & aSet0(all_14_2) = all_49_0 % 22.60/3.95 | | | | % 22.60/3.95 | | | | ALPHA: (65) implies: % 22.60/3.95 | | | | (66) ~ (all_49_0 = 0) % 22.60/3.95 | | | | (67) aSet0(all_14_2) = all_49_0 % 22.60/3.95 | | | | % 22.60/3.95 | | | | GROUND_INST: instantiating (6) with 0, all_49_0, all_14_2, simplifying % 22.60/3.95 | | | | with (10), (67) gives: % 22.60/3.95 | | | | (68) all_49_0 = 0 % 22.60/3.95 | | | | % 22.60/3.95 | | | | REDUCE: (66), (68) imply: % 22.60/3.95 | | | | (69) $false % 22.60/3.95 | | | | % 22.60/3.95 | | | | CLOSE: (69) is inconsistent. % 22.60/3.95 | | | | % 22.60/3.95 | | | End of split % 22.60/3.95 | | | % 22.60/3.95 | | End of split % 22.60/3.95 | | % 22.60/3.96 | Case 2: % 22.60/3.96 | | % 22.60/3.96 | | (70) ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.60/3.96 | | aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) % 22.60/3.96 | | % 22.60/3.96 | | ALPHA: (70) implies: % 22.60/3.96 | | (71) ~ (all_14_1 = 0) % 22.60/3.96 | | (72) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, % 22.60/3.96 | | all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) % 22.60/3.96 | | % 22.60/3.96 | | DELTA: instantiating (72) with fresh symbols all_40_0, all_40_1 gives: % 22.60/3.96 | | (73) ~ (all_40_0 = 0) & aElementOf0(all_40_1, all_14_2) = all_40_0 & % 22.60/3.96 | | aElementOf0(all_40_1, xS) = 0 & $i(all_40_1) % 22.60/3.96 | | % 22.60/3.96 | | ALPHA: (73) implies: % 22.60/3.96 | | (74) ~ (all_40_0 = 0) % 22.60/3.96 | | (75) $i(all_40_1) % 22.60/3.96 | | (76) aElementOf0(all_40_1, xS) = 0 % 22.60/3.96 | | (77) aElementOf0(all_40_1, all_14_2) = all_40_0 % 22.60/3.96 | | % 22.60/3.96 | | BETA: splitting (23) gives: % 22.60/3.96 | | % 22.60/3.96 | | Case 1: % 22.60/3.96 | | | % 22.60/3.96 | | | (78) all_14_1 = 0 % 22.60/3.96 | | | % 22.60/3.96 | | | REDUCE: (71), (78) imply: % 22.60/3.96 | | | (79) $false % 22.60/3.96 | | | % 22.60/3.96 | | | CLOSE: (79) is inconsistent. % 22.60/3.96 | | | % 22.60/3.96 | | Case 2: % 22.60/3.96 | | | % 22.60/3.96 | | | (80) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, % 22.60/3.96 | | | all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) | ? [v0: % 22.60/3.96 | | | int] : ( ~ (v0 = 0) & aSet0(xS) = v0) % 22.60/3.96 | | | % 22.60/3.96 | | | BETA: splitting (80) gives: % 22.60/3.96 | | | % 22.60/3.96 | | | Case 1: % 22.60/3.96 | | | | % 22.60/3.96 | | | | % 22.60/3.96 | | | | GROUND_INST: instantiating (16) with all_40_1, all_40_0, simplifying % 22.60/3.96 | | | | with (75), (77) gives: % 22.60/3.96 | | | | (81) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : % 22.60/3.96 | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, all_14_3) = v1 % 22.60/3.96 | | | | & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ~ (all_40_1 = xx)))) % 22.60/3.96 | | | | % 22.60/3.96 | | | | BETA: splitting (81) gives: % 22.60/3.96 | | | | % 22.60/3.96 | | | | Case 1: % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | (82) all_40_0 = 0 % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | REDUCE: (74), (82) imply: % 22.60/3.96 | | | | | (83) $false % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | CLOSE: (83) is inconsistent. % 22.60/3.96 | | | | | % 22.60/3.96 | | | | Case 2: % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | (84) ? [v0: any] : ? [v1: any] : (aElement0(all_40_1) = v0 & % 22.60/3.96 | | | | | aElementOf0(all_40_1, all_14_3) = v1 & ( ~ (v0 = 0) | ( ~ % 22.60/3.96 | | | | | (v1 = 0) & ~ (all_40_1 = xx)))) % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | DELTA: instantiating (84) with fresh symbols all_67_0, all_67_1 gives: % 22.60/3.96 | | | | | (85) aElement0(all_40_1) = all_67_1 & aElementOf0(all_40_1, % 22.60/3.96 | | | | | all_14_3) = all_67_0 & ( ~ (all_67_1 = 0) | ( ~ (all_67_0 = % 22.60/3.96 | | | | | 0) & ~ (all_40_1 = xx))) % 22.60/3.96 | | | | | % 22.60/3.96 | | | | | ALPHA: (85) implies: % 22.60/3.97 | | | | | (86) aElementOf0(all_40_1, all_14_3) = all_67_0 % 22.60/3.97 | | | | | (87) aElement0(all_40_1) = all_67_1 % 22.60/3.97 | | | | | (88) ~ (all_67_1 = 0) | ( ~ (all_67_0 = 0) & ~ (all_40_1 = xx)) % 22.60/3.97 | | | | | % 22.60/3.97 | | | | | GROUND_INST: instantiating (17) with all_40_1, all_67_0, simplifying % 22.60/3.97 | | | | | with (75), (86) gives: % 22.60/3.97 | | | | | (89) all_67_0 = 0 | all_40_1 = xx | ? [v0: any] : ? [v1: any] : % 22.60/3.97 | | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, xS) = v1 & ( % 22.60/3.97 | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 22.60/3.97 | | | | | % 22.60/3.97 | | | | | GROUND_INST: instantiating (18) with all_40_1, all_67_1, simplifying % 22.60/3.97 | | | | | with (75), (87) gives: % 22.60/3.97 | | | | | (90) all_67_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.60/3.97 | | | | | aElementOf0(all_40_1, xS) = v0) % 22.60/3.97 | | | | | % 22.60/3.97 | | | | | BETA: splitting (90) gives: % 22.60/3.97 | | | | | % 22.60/3.97 | | | | | Case 1: % 22.60/3.97 | | | | | | % 22.60/3.97 | | | | | | (91) all_67_1 = 0 % 22.60/3.97 | | | | | | % 22.60/3.97 | | | | | | REDUCE: (87), (91) imply: % 22.60/3.97 | | | | | | (92) aElement0(all_40_1) = 0 % 22.60/3.97 | | | | | | % 22.60/3.97 | | | | | | BETA: splitting (88) gives: % 22.60/3.97 | | | | | | % 22.60/3.97 | | | | | | Case 1: % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | (93) ~ (all_67_1 = 0) % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | REDUCE: (91), (93) imply: % 22.60/3.97 | | | | | | | (94) $false % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | CLOSE: (94) is inconsistent. % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | Case 2: % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | (95) ~ (all_67_0 = 0) & ~ (all_40_1 = xx) % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | ALPHA: (95) implies: % 22.60/3.97 | | | | | | | (96) ~ (all_40_1 = xx) % 22.60/3.97 | | | | | | | (97) ~ (all_67_0 = 0) % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | BETA: splitting (89) gives: % 22.60/3.97 | | | | | | | % 22.60/3.97 | | | | | | | Case 1: % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | (98) all_40_1 = xx % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | REDUCE: (96), (98) imply: % 22.60/3.97 | | | | | | | | (99) $false % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | CLOSE: (99) is inconsistent. % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | Case 2: % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | (100) all_67_0 = 0 | ? [v0: any] : ? [v1: any] : % 22.60/3.97 | | | | | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, xS) = % 22.60/3.97 | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | BETA: splitting (100) gives: % 22.60/3.97 | | | | | | | | % 22.60/3.97 | | | | | | | | Case 1: % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | (101) all_67_0 = 0 % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | REDUCE: (97), (101) imply: % 22.60/3.97 | | | | | | | | | (102) $false % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | CLOSE: (102) is inconsistent. % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | Case 2: % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | (103) ? [v0: any] : ? [v1: any] : (aElement0(all_40_1) = % 22.60/3.97 | | | | | | | | | v0 & aElementOf0(all_40_1, xS) = v1 & ( ~ (v1 = 0) % 22.60/3.97 | | | | | | | | | | ~ (v0 = 0))) % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_112_0, % 22.60/3.97 | | | | | | | | | all_112_1 gives: % 22.60/3.97 | | | | | | | | | (104) aElement0(all_40_1) = all_112_1 & % 22.60/3.97 | | | | | | | | | aElementOf0(all_40_1, xS) = all_112_0 & ( ~ % 22.60/3.97 | | | | | | | | | (all_112_0 = 0) | ~ (all_112_1 = 0)) % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | ALPHA: (104) implies: % 22.60/3.97 | | | | | | | | | (105) aElementOf0(all_40_1, xS) = all_112_0 % 22.60/3.97 | | | | | | | | | (106) aElement0(all_40_1) = all_112_1 % 22.60/3.97 | | | | | | | | | (107) ~ (all_112_0 = 0) | ~ (all_112_1 = 0) % 22.60/3.97 | | | | | | | | | % 22.60/3.97 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_112_0, xS, all_40_1, % 22.60/3.97 | | | | | | | | | simplifying with (76), (105) gives: % 22.60/3.97 | | | | | | | | | (108) all_112_0 = 0 % 22.60/3.97 | | | | | | | | | % 22.60/3.98 | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_112_1, all_40_1, % 22.60/3.98 | | | | | | | | | simplifying with (92), (106) gives: % 22.60/3.98 | | | | | | | | | (109) all_112_1 = 0 % 22.60/3.98 | | | | | | | | | % 22.60/3.98 | | | | | | | | | BETA: splitting (107) gives: % 22.60/3.98 | | | | | | | | | % 22.60/3.98 | | | | | | | | | Case 1: % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | (110) ~ (all_112_0 = 0) % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | REDUCE: (108), (110) imply: % 22.60/3.98 | | | | | | | | | | (111) $false % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | CLOSE: (111) is inconsistent. % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | Case 2: % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | (112) ~ (all_112_1 = 0) % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | REDUCE: (109), (112) imply: % 22.60/3.98 | | | | | | | | | | (113) $false % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | | CLOSE: (113) is inconsistent. % 22.60/3.98 | | | | | | | | | | % 22.60/3.98 | | | | | | | | | End of split % 22.60/3.98 | | | | | | | | | % 22.60/3.98 | | | | | | | | End of split % 22.60/3.98 | | | | | | | | % 22.60/3.98 | | | | | | | End of split % 22.60/3.98 | | | | | | | % 22.60/3.98 | | | | | | End of split % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | Case 2: % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | (114) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_40_1, xS) = % 22.60/3.98 | | | | | | v0) % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | DELTA: instantiating (114) with fresh symbol all_86_0 gives: % 22.60/3.98 | | | | | | (115) ~ (all_86_0 = 0) & aElementOf0(all_40_1, xS) = all_86_0 % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | ALPHA: (115) implies: % 22.60/3.98 | | | | | | (116) ~ (all_86_0 = 0) % 22.60/3.98 | | | | | | (117) aElementOf0(all_40_1, xS) = all_86_0 % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | GROUND_INST: instantiating (7) with 0, all_86_0, xS, all_40_1, % 22.60/3.98 | | | | | | simplifying with (76), (117) gives: % 22.60/3.98 | | | | | | (118) all_86_0 = 0 % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | REDUCE: (116), (118) imply: % 22.60/3.98 | | | | | | (119) $false % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | | CLOSE: (119) is inconsistent. % 22.60/3.98 | | | | | | % 22.60/3.98 | | | | | End of split % 22.60/3.98 | | | | | % 22.60/3.98 | | | | End of split % 22.60/3.98 | | | | % 22.60/3.98 | | | Case 2: % 22.60/3.98 | | | | % 22.60/3.98 | | | | (120) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xS) = v0) % 22.60/3.98 | | | | % 22.60/3.98 | | | | DELTA: instantiating (120) with fresh symbol all_49_0 gives: % 22.60/3.98 | | | | (121) ~ (all_49_0 = 0) & aSet0(xS) = all_49_0 % 22.60/3.98 | | | | % 22.60/3.98 | | | | ALPHA: (121) implies: % 22.60/3.98 | | | | (122) ~ (all_49_0 = 0) % 22.60/3.98 | | | | (123) aSet0(xS) = all_49_0 % 22.60/3.98 | | | | % 22.60/3.98 | | | | GROUND_INST: instantiating (6) with 0, all_49_0, xS, simplifying with % 22.60/3.98 | | | | (1), (123) gives: % 22.60/3.98 | | | | (124) all_49_0 = 0 % 22.60/3.98 | | | | % 22.60/3.98 | | | | REDUCE: (122), (124) imply: % 22.60/3.98 | | | | (125) $false % 22.60/3.98 | | | | % 22.60/3.98 | | | | CLOSE: (125) is inconsistent. % 22.60/3.98 | | | | % 22.60/3.98 | | | End of split % 22.60/3.98 | | | % 22.60/3.98 | | End of split % 22.60/3.98 | | % 22.60/3.98 | End of split % 22.60/3.98 | % 22.60/3.98 End of proof % 22.60/3.98 % 22.60/3.98 Sub-proof #1 shows that the following formulas are inconsistent: % 22.60/3.98 ---------------------------------------------------------------- % 22.60/3.98 (1) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 & aElementOf0(all_40_1, xS) % 22.60/3.98 = 0 % 22.60/3.98 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.60/3.98 ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 22.60/3.98 (aElementOf0(v3, v2) = v0)) % 22.60/3.98 (3) aElementOf0(all_40_1, xS) = all_40_0 % 22.60/3.98 (4) ~ (all_40_0 = 0) % 22.60/3.98 % 22.60/3.98 Begin of proof % 22.60/3.98 | % 22.60/3.98 | ALPHA: (1) implies: % 22.60/3.98 | (5) aElementOf0(all_40_1, xS) = 0 % 22.60/3.98 | % 22.60/3.98 | GROUND_INST: instantiating (2) with all_40_0, 0, xS, all_40_1, simplifying % 22.60/3.98 | with (3), (5) gives: % 22.60/3.98 | (6) all_40_0 = 0 % 22.60/3.98 | % 22.60/3.98 | REDUCE: (4), (6) imply: % 22.60/3.98 | (7) $false % 22.60/3.98 | % 22.60/3.98 | CLOSE: (7) is inconsistent. % 22.60/3.98 | % 22.60/3.98 End of proof % 22.60/3.98 % SZS output end Proof for theBenchmark % 22.60/3.99 % 22.60/3.99 3392ms %------------------------------------------------------------------------------