%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM533+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 : n012.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 6.13s 1.63s % Output : Proof 8.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM533+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n012.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Fri Aug 25 11:12:11 EDT 2023 % 0.16/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.43/1.05 Prover 4: Preprocessing ... % 2.43/1.05 Prover 1: Preprocessing ... % 2.60/1.09 Prover 2: Preprocessing ... % 2.60/1.09 Prover 3: Preprocessing ... % 2.60/1.09 Prover 6: Preprocessing ... % 2.60/1.09 Prover 5: Preprocessing ... % 2.60/1.09 Prover 0: Preprocessing ... % 4.09/1.30 Prover 2: Constructing countermodel ... % 4.09/1.30 Prover 5: Constructing countermodel ... % 4.09/1.34 Prover 1: Constructing countermodel ... % 4.09/1.37 Prover 3: Constructing countermodel ... % 4.09/1.39 Prover 6: Proving ... % 5.04/1.43 Prover 4: Constructing countermodel ... % 5.25/1.52 Prover 0: Proving ... % 6.13/1.63 Prover 3: proved (951ms) % 6.13/1.63 % 6.13/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.13/1.63 % 6.13/1.63 Prover 2: stopped % 6.13/1.63 Prover 5: stopped % 6.61/1.65 Prover 0: stopped % 6.83/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.83/1.67 Prover 6: stopped % 6.83/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.83/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.83/1.67 Prover 7: Preprocessing ... % 6.83/1.67 Prover 8: Preprocessing ... % 6.83/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.83/1.68 Prover 10: Preprocessing ... % 6.83/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.83/1.69 Prover 11: Preprocessing ... % 6.83/1.71 Prover 13: Preprocessing ... % 6.83/1.71 Prover 7: Constructing countermodel ... % 7.28/1.74 Prover 10: Constructing countermodel ... % 7.28/1.75 Prover 1: Found proof (size 40) % 7.28/1.75 Prover 1: proved (1075ms) % 7.28/1.75 Prover 10: stopped % 7.28/1.75 Prover 7: stopped % 7.28/1.75 Prover 4: stopped % 7.28/1.76 Prover 13: Constructing countermodel ... % 7.54/1.76 Prover 13: stopped % 7.54/1.77 Prover 8: Warning: ignoring some quantifiers % 7.54/1.77 Prover 8: Constructing countermodel ... % 7.54/1.78 Prover 8: stopped % 7.54/1.82 Prover 11: Constructing countermodel ... % 7.54/1.82 Prover 11: stopped % 7.54/1.82 % 7.54/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.54/1.82 % 7.54/1.83 % SZS output start Proof for theBenchmark % 7.92/1.83 Assumptions after simplification: % 7.92/1.83 --------------------------------- % 7.92/1.83 % 7.92/1.83 (mDefSub) % 7.92/1.86 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] : % 7.92/1.86 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 7.92/1.86 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) = % 7.92/1.86 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & ! % 7.92/1.86 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & ! % 7.92/1.86 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ % 7.92/1.86 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) = % 7.92/1.86 v4)))))) % 7.92/1.86 % 7.92/1.86 (m__) % 7.92/1.87 $i(xC) & $i(xB) & $i(xA) & ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) = % 7.92/1.87 0 & aSubsetOf0(xA, xC) = v0 & aSubsetOf0(xA, xB) = 0 & ! [v1: $i] : ! [v2: % 7.92/1.87 int] : (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~ $i(v1) | ? [v3: int] % 7.92/1.87 : ( ~ (v3 = 0) & aElementOf0(v1, xB) = v3)) & ! [v1: $i] : ! [v2: int] : % 7.92/1.87 (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 % 7.92/1.87 = 0) & aElementOf0(v1, xA) = v3)) & ? [v1: $i] : ? [v2: int] : ( ~ % 7.92/1.87 (v2 = 0) & aElementOf0(v1, xC) = v2 & aElementOf0(v1, xA) = 0 & $i(v1))) % 7.92/1.87 % 7.92/1.87 (m__522) % 7.92/1.87 aSet0(xC) = 0 & aSet0(xB) = 0 & aSet0(xA) = 0 & $i(xC) & $i(xB) & $i(xA) % 7.92/1.87 % 7.92/1.87 (function-axioms) % 8.10/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.10/1.87 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = % 8.10/1.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.10/1.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 8.10/1.87 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | % 8.10/1.87 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 8.10/1.87 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 8.10/1.87 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 8.10/1.87 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 8.10/1.87 % 8.10/1.87 Further assumptions not needed in the proof: % 8.10/1.87 -------------------------------------------- % 8.10/1.87 mCntRel, mCountNFin, mCountNFin_01, mDefEmp, mEOfElem, mElmSort, mEmpFin, % 8.10/1.87 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl % 8.10/1.87 % 8.10/1.87 Those formulas are unsatisfiable: % 8.10/1.87 --------------------------------- % 8.10/1.87 % 8.10/1.87 Begin of proof % 8.10/1.88 | % 8.10/1.88 | ALPHA: (m__522) implies: % 8.10/1.88 | (1) aSet0(xB) = 0 % 8.10/1.88 | (2) aSet0(xC) = 0 % 8.10/1.88 | % 8.10/1.88 | ALPHA: (m__) implies: % 8.10/1.88 | (3) $i(xA) % 8.10/1.88 | (4) $i(xB) % 8.10/1.88 | (5) $i(xC) % 8.10/1.88 | (6) ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA, % 8.10/1.88 | xC) = v0 & aSubsetOf0(xA, xB) = 0 & ! [v1: $i] : ! [v2: int] : % 8.10/1.88 | (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~ $i(v1) | ? [v3: int] : % 8.10/1.88 | ( ~ (v3 = 0) & aElementOf0(v1, xB) = v3)) & ! [v1: $i] : ! [v2: % 8.10/1.88 | int] : (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~ $i(v1) | ? % 8.10/1.88 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xA) = v3)) & ? [v1: $i] % 8.10/1.88 | : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, xC) = v2 & % 8.10/1.88 | aElementOf0(v1, xA) = 0 & $i(v1))) % 8.10/1.88 | % 8.10/1.88 | ALPHA: (function-axioms) implies: % 8.10/1.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.10/1.88 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 8.10/1.89 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.10/1.89 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 8.10/1.89 | (aElementOf0(v3, v2) = v0)) % 8.10/1.89 | % 8.10/1.89 | DELTA: instantiating (6) with fresh symbol all_11_0 gives: % 8.10/1.89 | (9) ~ (all_11_0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA, xC) = % 8.10/1.89 | all_11_0 & aSubsetOf0(xA, xB) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = % 8.10/1.89 | 0 | ~ (aElementOf0(v0, xC) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 8.10/1.89 | (v2 = 0) & aElementOf0(v0, xB) = v2)) & ! [v0: $i] : ! [v1: int] % 8.10/1.89 | : (v1 = 0 | ~ (aElementOf0(v0, xB) = v1) | ~ $i(v0) | ? [v2: int] : % 8.10/1.89 | ( ~ (v2 = 0) & aElementOf0(v0, xA) = v2)) & ? [v0: $i] : ? [v1: % 8.10/1.89 | int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = v1 & aElementOf0(v0, xA) % 8.10/1.89 | = 0 & $i(v0)) % 8.10/1.89 | % 8.10/1.89 | ALPHA: (9) implies: % 8.10/1.89 | (10) ~ (all_11_0 = 0) % 8.10/1.89 | (11) aSubsetOf0(xA, xB) = 0 % 8.10/1.89 | (12) aSubsetOf0(xA, xC) = all_11_0 % 8.10/1.89 | (13) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xC) = v1) | % 8.10/1.89 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xB) = v2)) % 8.10/1.89 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = v1 & % 8.10/1.89 | aElementOf0(v0, xA) = 0 & $i(v0)) % 8.10/1.89 | % 8.10/1.89 | DELTA: instantiating (14) with fresh symbols all_14_0, all_14_1 gives: % 8.10/1.89 | (15) ~ (all_14_0 = 0) & aElementOf0(all_14_1, xC) = all_14_0 & % 8.10/1.89 | aElementOf0(all_14_1, xA) = 0 & $i(all_14_1) % 8.10/1.89 | % 8.10/1.89 | ALPHA: (15) implies: % 8.10/1.89 | (16) ~ (all_14_0 = 0) % 8.10/1.89 | (17) $i(all_14_1) % 8.10/1.89 | (18) aElementOf0(all_14_1, xA) = 0 % 8.10/1.89 | (19) aElementOf0(all_14_1, xC) = all_14_0 % 8.10/1.89 | % 8.10/1.89 | GROUND_INST: instantiating (13) with all_14_1, all_14_0, simplifying with % 8.10/1.89 | (17), (19) gives: % 8.10/1.89 | (20) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xB) % 8.10/1.90 | = v0) % 8.10/1.90 | % 8.10/1.90 | GROUND_INST: instantiating (mDefSub) with xB, simplifying with (1), (4) gives: % 8.10/1.90 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xB) = v1) | % 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xB) = v3 & $i(v2)) | ? % 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 8.10/1.90 | (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] % 8.10/1.90 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~ % 8.10/1.90 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) = % 8.10/1.90 | v3)))) % 8.10/1.90 | % 8.10/1.90 | ALPHA: (21) implies: % 8.10/1.90 | (22) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) = % 8.10/1.90 | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB) % 8.10/1.90 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 8.10/1.90 | aElementOf0(v1, v0) = v3)))) % 8.10/1.90 | % 8.10/1.90 | GROUND_INST: instantiating (mDefSub) with xC, simplifying with (2), (5) gives: % 8.10/1.90 | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) | % 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ? % 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 8.10/1.90 | (aSubsetOf0(v0, xC) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] % 8.10/1.90 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~ % 8.10/1.90 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) = % 8.10/1.90 | v3)))) % 8.10/1.90 | % 8.10/1.90 | ALPHA: (23) implies: % 8.10/1.90 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) | % 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ? % 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) % 8.10/1.90 | % 8.10/1.90 | GROUND_INST: instantiating (24) with xA, all_11_0, simplifying with (3), (12) % 8.10/1.90 | gives: % 8.10/1.90 | (25) all_11_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.10/1.90 | aElementOf0(v0, xC) = v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ? % 8.10/1.90 | [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0) % 8.10/1.90 | % 8.10/1.90 | GROUND_INST: instantiating (22) with xA, simplifying with (3), (11) gives: % 8.10/1.91 | (26) aSet0(xA) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 8.10/1.91 | (aElementOf0(v0, xB) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 8.10/1.91 | & aElementOf0(v0, xA) = v2)) % 8.10/1.91 | % 8.10/1.91 | ALPHA: (26) implies: % 8.10/1.91 | (27) aSet0(xA) = 0 % 8.10/1.91 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xB) = v1) | % 8.10/1.91 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xA) = v2)) % 8.10/1.91 | % 8.10/1.91 | BETA: splitting (20) gives: % 8.10/1.91 | % 8.10/1.91 | Case 1: % 8.10/1.91 | | % 8.10/1.91 | | (29) all_14_0 = 0 % 8.10/1.91 | | % 8.10/1.91 | | REDUCE: (16), (29) imply: % 8.10/1.91 | | (30) $false % 8.10/1.91 | | % 8.10/1.91 | | CLOSE: (30) is inconsistent. % 8.10/1.91 | | % 8.10/1.91 | Case 2: % 8.10/1.91 | | % 8.10/1.91 | | (31) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xB) = v0) % 8.10/1.91 | | % 8.10/1.91 | | DELTA: instantiating (31) with fresh symbol all_35_0 gives: % 8.10/1.91 | | (32) ~ (all_35_0 = 0) & aElementOf0(all_14_1, xB) = all_35_0 % 8.10/1.91 | | % 8.10/1.91 | | ALPHA: (32) implies: % 8.10/1.91 | | (33) ~ (all_35_0 = 0) % 8.10/1.91 | | (34) aElementOf0(all_14_1, xB) = all_35_0 % 8.10/1.91 | | % 8.10/1.91 | | BETA: splitting (25) gives: % 8.10/1.91 | | % 8.10/1.91 | | Case 1: % 8.10/1.91 | | | % 8.10/1.91 | | | (35) all_11_0 = 0 % 8.10/1.91 | | | % 8.10/1.91 | | | REDUCE: (10), (35) imply: % 8.10/1.91 | | | (36) $false % 8.10/1.91 | | | % 8.10/1.91 | | | CLOSE: (36) is inconsistent. % 8.10/1.91 | | | % 8.10/1.91 | | Case 2: % 8.10/1.91 | | | % 8.10/1.91 | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = % 8.10/1.91 | | | v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0 % 8.10/1.91 | | | = 0) & aSet0(xA) = v0) % 8.10/1.91 | | | % 8.10/1.91 | | | BETA: splitting (37) gives: % 8.10/1.91 | | | % 8.10/1.91 | | | Case 1: % 8.10/1.91 | | | | % 8.10/1.91 | | | | % 8.10/1.91 | | | | GROUND_INST: instantiating (28) with all_14_1, all_35_0, simplifying % 8.10/1.91 | | | | with (17), (34) gives: % 8.10/1.91 | | | | (38) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 8.10/1.91 | | | | aElementOf0(all_14_1, xA) = v0) % 8.10/1.91 | | | | % 8.10/1.91 | | | | BETA: splitting (38) gives: % 8.10/1.91 | | | | % 8.10/1.91 | | | | Case 1: % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | (39) all_35_0 = 0 % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | REDUCE: (33), (39) imply: % 8.10/1.91 | | | | | (40) $false % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | CLOSE: (40) is inconsistent. % 8.10/1.91 | | | | | % 8.10/1.91 | | | | Case 2: % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | (41) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xA) = v0) % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | DELTA: instantiating (41) with fresh symbol all_58_0 gives: % 8.10/1.91 | | | | | (42) ~ (all_58_0 = 0) & aElementOf0(all_14_1, xA) = all_58_0 % 8.10/1.91 | | | | | % 8.10/1.91 | | | | | ALPHA: (42) implies: % 8.10/1.91 | | | | | (43) ~ (all_58_0 = 0) % 8.10/1.92 | | | | | (44) aElementOf0(all_14_1, xA) = all_58_0 % 8.10/1.92 | | | | | % 8.10/1.92 | | | | | GROUND_INST: instantiating (8) with 0, all_58_0, xA, all_14_1, % 8.10/1.92 | | | | | simplifying with (18), (44) gives: % 8.10/1.92 | | | | | (45) all_58_0 = 0 % 8.10/1.92 | | | | | % 8.10/1.92 | | | | | REDUCE: (43), (45) imply: % 8.10/1.92 | | | | | (46) $false % 8.10/1.92 | | | | | % 8.10/1.92 | | | | | CLOSE: (46) is inconsistent. % 8.10/1.92 | | | | | % 8.10/1.92 | | | | End of split % 8.10/1.92 | | | | % 8.10/1.92 | | | Case 2: % 8.10/1.92 | | | | % 8.10/1.92 | | | | (47) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0) % 8.10/1.92 | | | | % 8.10/1.92 | | | | DELTA: instantiating (47) with fresh symbol all_43_0 gives: % 8.10/1.92 | | | | (48) ~ (all_43_0 = 0) & aSet0(xA) = all_43_0 % 8.10/1.92 | | | | % 8.10/1.92 | | | | ALPHA: (48) implies: % 8.10/1.92 | | | | (49) ~ (all_43_0 = 0) % 8.10/1.92 | | | | (50) aSet0(xA) = all_43_0 % 8.10/1.92 | | | | % 8.10/1.92 | | | | GROUND_INST: instantiating (7) with 0, all_43_0, xA, simplifying with % 8.10/1.92 | | | | (27), (50) gives: % 8.10/1.92 | | | | (51) all_43_0 = 0 % 8.10/1.92 | | | | % 8.10/1.92 | | | | REDUCE: (49), (51) imply: % 8.10/1.92 | | | | (52) $false % 8.10/1.92 | | | | % 8.10/1.92 | | | | CLOSE: (52) is inconsistent. % 8.10/1.92 | | | | % 8.10/1.92 | | | End of split % 8.10/1.92 | | | % 8.10/1.92 | | End of split % 8.10/1.92 | | % 8.10/1.92 | End of split % 8.10/1.92 | % 8.10/1.92 End of proof % 8.10/1.92 % SZS output end Proof for theBenchmark % 8.10/1.92 % 8.10/1.92 1272ms %------------------------------------------------------------------------------