%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET802+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 15:26:30 EDT 2023 % Result : Theorem 10.57s 2.24s % Output : Proof 12.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET802+4 : TPTP v8.1.2. Released v3.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 16:29:38 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.13/1.15 Prover 1: Preprocessing ... % 3.13/1.15 Prover 4: Preprocessing ... % 3.30/1.19 Prover 6: Preprocessing ... % 3.30/1.19 Prover 2: Preprocessing ... % 3.30/1.19 Prover 3: Preprocessing ... % 3.30/1.19 Prover 5: Preprocessing ... % 3.30/1.19 Prover 0: Preprocessing ... % 7.18/1.73 Prover 5: Proving ... % 7.62/1.79 Prover 2: Proving ... % 8.25/1.87 Prover 3: Constructing countermodel ... % 8.25/1.88 Prover 6: Proving ... % 8.25/1.89 Prover 1: Constructing countermodel ... % 8.57/2.02 Prover 4: Constructing countermodel ... % 8.86/2.10 Prover 0: Proving ... % 10.57/2.23 Prover 3: proved (1598ms) % 10.57/2.23 % 10.57/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.57/2.24 % 10.57/2.24 Prover 6: stopped % 10.57/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.57/2.24 Prover 5: stopped % 10.57/2.25 Prover 0: stopped % 10.57/2.26 Prover 2: stopped % 10.57/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.57/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.00/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.00/2.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.00/2.28 Prover 7: Preprocessing ... % 11.00/2.30 Prover 8: Preprocessing ... % 11.00/2.31 Prover 10: Preprocessing ... % 11.00/2.32 Prover 11: Preprocessing ... % 11.00/2.33 Prover 13: Preprocessing ... % 11.00/2.35 Prover 1: Found proof (size 87) % 11.00/2.35 Prover 1: proved (1727ms) % 11.00/2.35 Prover 4: stopped % 11.66/2.35 Prover 10: stopped % 11.66/2.37 Prover 13: stopped % 11.66/2.38 Prover 7: Warning: ignoring some quantifiers % 11.66/2.39 Prover 11: stopped % 11.93/2.40 Prover 7: Constructing countermodel ... % 11.93/2.41 Prover 7: stopped % 12.17/2.47 Prover 8: Warning: ignoring some quantifiers % 12.17/2.47 Prover 8: Constructing countermodel ... % 12.17/2.48 Prover 8: stopped % 12.17/2.48 % 12.17/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.17/2.48 % 12.17/2.49 % SZS output start Proof for theBenchmark % 12.17/2.49 Assumptions after simplification: % 12.17/2.49 --------------------------------- % 12.17/2.50 % 12.17/2.50 (greatest_lower_bound) % 12.46/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.46/2.52 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 12.46/2.52 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 12.46/2.52 lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 & member(v5, v3) = 0 % 12.46/2.52 & $i(v5)) | ? [v5: any] : ? [v6: any] : (lower_bound(v0, v2, v1) = v6 & % 12.46/2.52 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 12.46/2.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (greatest_lower_bound(v0, v1, v2, % 12.46/2.52 v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.46/2.52 (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~ % 12.46/2.52 (lower_bound(v4, v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] % 12.46/2.52 : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = % 12.46/2.52 0))))) % 12.46/2.52 % 12.46/2.52 (least) % 12.46/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.46/2.53 (least(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 12.46/2.53 ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0 & % 12.46/2.53 $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 12.46/2.53 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) | ~ $i(v2) | % 12.46/2.53 ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : ! [v4: int] : % 12.46/2.53 (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 12.46/2.53 = 0) & member(v3, v1) = v5)))) % 12.46/2.53 % 12.46/2.53 (lower_bound) % 12.46/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.46/2.53 (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 12.46/2.53 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, % 12.46/2.53 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.46/2.53 (lower_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: % 12.46/2.53 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | % 12.46/2.53 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 12.46/2.53 % 12.46/2.53 (thIV14) % 12.46/2.53 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 12.46/2.53 : (subset(v2, v1) = 0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 12.46/2.53 ? [v6: any] : (greatest_lower_bound(v3, v2, v0, v1) = v6 & least(v3, v0, % 12.46/2.53 v2) = v4 & member(v3, v2) = v5 & $i(v3) & ((v6 = 0 & v5 = 0 & ~ (v4 = % 12.46/2.53 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0))))))) % 12.46/2.53 % 12.46/2.53 (function-axioms) % 12.46/2.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.46/2.54 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 12.46/2.54 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 12.46/2.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.46/2.54 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 12.46/2.54 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 12.46/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.46/2.54 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 12.46/2.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.46/2.54 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 12.46/2.54 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.46/2.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.46/2.54 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 12.46/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.46/2.54 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 12.46/2.54 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.46/2.54 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 12.46/2.54 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 12.46/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.46/2.54 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 12.46/2.54 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.46/2.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.46/2.54 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 12.46/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.46/2.54 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 12.46/2.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.46/2.54 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 12.46/2.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.54 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 12.46/2.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.54 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 12.46/2.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 12.46/2.54 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.46/2.54 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 12.46/2.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.46/2.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 12.46/2.54 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.46/2.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 12.46/2.54 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.46/2.54 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.54 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 12.46/2.54 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 12.46/2.54 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 12.46/2.54 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 12.46/2.54 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 12.46/2.54 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 12.46/2.54 (power_set(v2) = v0)) % 12.46/2.54 % 12.46/2.54 Further assumptions not needed in the proof: % 12.46/2.54 -------------------------------------------- % 12.46/2.54 difference, empty_set, equal_set, greatest, intersection, least_upper_bound, % 12.46/2.54 max, min, order, power_set, product, singleton, subset, sum, total_order, union, % 12.46/2.54 unordered_pair, upper_bound % 12.46/2.54 % 12.46/2.54 Those formulas are unsatisfiable: % 12.46/2.54 --------------------------------- % 12.46/2.54 % 12.46/2.54 Begin of proof % 12.46/2.54 | % 12.46/2.54 | ALPHA: (lower_bound) implies: % 12.46/2.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (lower_bound(v2, v0, v1) % 12.46/2.55 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: % 12.46/2.55 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5: % 12.46/2.55 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 12.46/2.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.46/2.55 | (lower_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.46/2.55 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & % 12.46/2.55 | member(v4, v1) = 0 & $i(v4))) % 12.46/2.55 | % 12.46/2.55 | ALPHA: (least) implies: % 12.46/2.55 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) | % 12.46/2.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] % 12.46/2.55 | : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) % 12.46/2.55 | | ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))) % 12.46/2.55 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.46/2.55 | (least(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 12.46/2.55 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & % 12.46/2.55 | member(v4, v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & % 12.46/2.55 | member(v2, v1) = v4)) % 12.46/2.55 | % 12.46/2.55 | ALPHA: (greatest_lower_bound) implies: % 12.46/2.55 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.46/2.55 | (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | % 12.46/2.55 | ~ $i(v1) | ~ $i(v0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) % 12.46/2.55 | = 0 & ! [v4: $i] : ( ~ (lower_bound(v4, v2, v1) = 0) | ~ $i(v4) | % 12.46/2.55 | ? [v5: any] : ? [v6: any] : (apply(v2, v4, v0) = v6 & % 12.46/2.55 | member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))))) % 12.46/2.55 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.46/2.55 | (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | % 12.46/2.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ % 12.46/2.55 | (v6 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v6 & % 12.46/2.55 | member(v5, v3) = 0 & $i(v5)) | ? [v5: any] : ? [v6: any] : % 12.46/2.55 | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | % 12.46/2.55 | ~ (v5 = 0)))) % 12.46/2.55 | % 12.46/2.55 | ALPHA: (function-axioms) implies: % 12.46/2.55 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.46/2.55 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 12.46/2.55 | = v0)) % 12.46/2.55 | % 12.46/2.55 | DELTA: instantiating (thIV14) with fresh symbols all_25_0, all_25_1 gives: % 12.46/2.55 | (8) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0: % 12.46/2.55 | $i] : (subset(v0, all_25_0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 12.46/2.55 | : ? [v3: any] : ? [v4: any] : (greatest_lower_bound(v1, v0, % 12.46/2.55 | all_25_1, all_25_0) = v4 & least(v1, all_25_1, v0) = v2 & % 12.46/2.56 | member(v1, v0) = v3 & $i(v1) & ((v4 = 0 & v3 = 0 & ~ (v2 = 0)) | % 12.46/2.56 | (v2 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) % 12.46/2.56 | % 12.46/2.56 | ALPHA: (8) implies: % 12.46/2.56 | (9) $i(all_25_1) % 12.46/2.56 | (10) $i(all_25_0) % 12.75/2.56 | (11) ? [v0: $i] : (subset(v0, all_25_0) = 0 & $i(v0) & ? [v1: $i] : ? % 12.75/2.56 | [v2: any] : ? [v3: any] : ? [v4: any] : (greatest_lower_bound(v1, % 12.75/2.56 | v0, all_25_1, all_25_0) = v4 & least(v1, all_25_1, v0) = v2 & % 12.75/2.56 | member(v1, v0) = v3 & $i(v1) & ((v4 = 0 & v3 = 0 & ~ (v2 = 0)) | % 12.75/2.56 | (v2 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) % 12.75/2.56 | % 12.75/2.56 | DELTA: instantiating (11) with fresh symbol all_27_0 gives: % 12.75/2.56 | (12) subset(all_27_0, all_25_0) = 0 & $i(all_27_0) & ? [v0: $i] : ? [v1: % 12.75/2.56 | any] : ? [v2: any] : ? [v3: any] : (greatest_lower_bound(v0, % 12.75/2.56 | all_27_0, all_25_1, all_25_0) = v3 & least(v0, all_25_1, all_27_0) % 12.75/2.56 | = v1 & member(v0, all_27_0) = v2 & $i(v0) & ((v3 = 0 & v2 = 0 & ~ % 12.75/2.56 | (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 12.75/2.56 | % 12.75/2.56 | ALPHA: (12) implies: % 12.75/2.56 | (13) $i(all_27_0) % 12.75/2.56 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 12.75/2.56 | (greatest_lower_bound(v0, all_27_0, all_25_1, all_25_0) = v3 & % 12.75/2.56 | least(v0, all_25_1, all_27_0) = v1 & member(v0, all_27_0) = v2 & % 12.75/2.56 | $i(v0) & ((v3 = 0 & v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ( ~ (v3 = 0) | % 12.75/2.56 | ~ (v2 = 0))))) % 12.75/2.56 | % 12.75/2.56 | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1, all_29_2, % 12.75/2.56 | all_29_3 gives: % 12.75/2.56 | (15) greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) = % 12.75/2.56 | all_29_0 & least(all_29_3, all_25_1, all_27_0) = all_29_2 & % 12.75/2.56 | member(all_29_3, all_27_0) = all_29_1 & $i(all_29_3) & ((all_29_0 = 0 % 12.75/2.56 | & all_29_1 = 0 & ~ (all_29_2 = 0)) | (all_29_2 = 0 & ( ~ % 12.75/2.56 | (all_29_0 = 0) | ~ (all_29_1 = 0)))) % 12.75/2.56 | % 12.75/2.56 | ALPHA: (15) implies: % 12.75/2.56 | (16) $i(all_29_3) % 12.75/2.56 | (17) member(all_29_3, all_27_0) = all_29_1 % 12.75/2.56 | (18) least(all_29_3, all_25_1, all_27_0) = all_29_2 % 12.75/2.56 | (19) greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) = % 12.75/2.56 | all_29_0 % 12.75/2.56 | (20) (all_29_0 = 0 & all_29_1 = 0 & ~ (all_29_2 = 0)) | (all_29_2 = 0 & ( % 12.75/2.56 | ~ (all_29_0 = 0) | ~ (all_29_1 = 0))) % 12.75/2.56 | % 12.75/2.56 | GROUND_INST: instantiating (4) with all_25_1, all_27_0, all_29_3, all_29_2, % 12.75/2.56 | simplifying with (9), (13), (16), (18) gives: % 12.75/2.56 | (21) all_29_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.75/2.56 | apply(all_25_1, all_29_3, v0) = v1 & member(v0, all_27_0) = 0 & % 12.75/2.56 | $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = % 12.75/2.56 | v0) % 12.75/2.56 | % 12.75/2.56 | GROUND_INST: instantiating (6) with all_29_3, all_27_0, all_25_1, all_25_0, % 12.75/2.56 | all_29_0, simplifying with (9), (10), (13), (16), (19) gives: % 12.75/2.57 | (22) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.75/2.57 | lower_bound(v0, all_25_1, all_27_0) = 0 & apply(all_25_1, v0, % 12.75/2.57 | all_29_3) = v1 & member(v0, all_25_0) = 0 & $i(v0)) | ? [v0: any] % 12.75/2.57 | : ? [v1: any] : (lower_bound(all_29_3, all_25_1, all_27_0) = v1 & % 12.75/2.57 | member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.75/2.57 | % 12.75/2.57 | BETA: splitting (20) gives: % 12.75/2.57 | % 12.75/2.57 | Case 1: % 12.75/2.57 | | % 12.75/2.57 | | (23) all_29_0 = 0 & all_29_1 = 0 & ~ (all_29_2 = 0) % 12.75/2.57 | | % 12.75/2.57 | | ALPHA: (23) implies: % 12.75/2.57 | | (24) all_29_1 = 0 % 12.75/2.57 | | (25) all_29_0 = 0 % 12.75/2.57 | | (26) ~ (all_29_2 = 0) % 12.75/2.57 | | % 12.75/2.57 | | REDUCE: (19), (25) imply: % 12.75/2.57 | | (27) greatest_lower_bound(all_29_3, all_27_0, all_25_1, all_25_0) = 0 % 12.75/2.57 | | % 12.75/2.57 | | REDUCE: (17), (24) imply: % 12.75/2.57 | | (28) member(all_29_3, all_27_0) = 0 % 12.75/2.57 | | % 12.75/2.57 | | BETA: splitting (21) gives: % 12.75/2.57 | | % 12.75/2.57 | | Case 1: % 12.75/2.57 | | | % 12.75/2.57 | | | (29) all_29_2 = 0 % 12.75/2.57 | | | % 12.75/2.57 | | | REDUCE: (26), (29) imply: % 12.75/2.57 | | | (30) $false % 12.75/2.57 | | | % 12.75/2.57 | | | CLOSE: (30) is inconsistent. % 12.75/2.57 | | | % 12.75/2.57 | | Case 2: % 12.75/2.57 | | | % 12.75/2.57 | | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, % 12.75/2.57 | | | all_29_3, v0) = v1 & member(v0, all_27_0) = 0 & $i(v0)) | ? % 12.75/2.57 | | | [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0) % 12.75/2.57 | | | % 12.75/2.57 | | | BETA: splitting (31) gives: % 12.75/2.57 | | | % 12.75/2.57 | | | Case 1: % 12.75/2.57 | | | | % 12.75/2.57 | | | | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, % 12.75/2.57 | | | | all_29_3, v0) = v1 & member(v0, all_27_0) = 0 & $i(v0)) % 12.75/2.57 | | | | % 12.75/2.57 | | | | GROUND_INST: instantiating (5) with all_29_3, all_27_0, all_25_1, % 12.75/2.57 | | | | all_25_0, simplifying with (9), (10), (13), (16), (27) % 12.75/2.57 | | | | gives: % 12.75/2.57 | | | | (33) lower_bound(all_29_3, all_25_1, all_27_0) = 0 & member(all_29_3, % 12.75/2.57 | | | | all_27_0) = 0 & ! [v0: $i] : ( ~ (lower_bound(v0, all_25_1, % 12.75/2.57 | | | | all_27_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 12.75/2.57 | | | | (apply(all_25_1, v0, all_29_3) = v2 & member(v0, all_25_0) = % 12.75/2.57 | | | | v1 & ( ~ (v1 = 0) | v2 = 0))) % 12.75/2.57 | | | | % 12.75/2.57 | | | | ALPHA: (33) implies: % 12.75/2.57 | | | | (34) lower_bound(all_29_3, all_25_1, all_27_0) = 0 % 12.75/2.57 | | | | % 12.75/2.57 | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_29_3, % 12.75/2.57 | | | | simplifying with (9), (13), (16), (34) gives: % 12.75/2.57 | | | | (35) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, % 12.75/2.57 | | | | all_29_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 12.75/2.57 | | | | 0) & member(v0, all_27_0) = v2)) % 12.75/2.57 | | | | % 12.75/2.57 | | | | DELTA: instantiating (32) with fresh symbols all_94_0, all_94_1 gives: % 12.75/2.57 | | | | (36) ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) = % 12.75/2.57 | | | | all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1) % 12.75/2.57 | | | | % 12.75/2.57 | | | | REF_CLOSE: (7), (35), (36) are inconsistent by sub-proof #2. % 12.75/2.57 | | | | % 12.75/2.57 | | | Case 2: % 12.75/2.57 | | | | % 12.75/2.58 | | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = v0) % 12.75/2.58 | | | | % 12.75/2.58 | | | | DELTA: instantiating (37) with fresh symbol all_89_0 gives: % 12.75/2.58 | | | | (38) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0 % 12.75/2.58 | | | | % 12.75/2.58 | | | | REF_CLOSE: (7), (28), (38) are inconsistent by sub-proof #1. % 12.75/2.58 | | | | % 12.75/2.58 | | | End of split % 12.75/2.58 | | | % 12.75/2.58 | | End of split % 12.75/2.58 | | % 12.75/2.58 | Case 2: % 12.75/2.58 | | % 12.75/2.58 | | (39) all_29_2 = 0 & ( ~ (all_29_0 = 0) | ~ (all_29_1 = 0)) % 12.75/2.58 | | % 12.75/2.58 | | ALPHA: (39) implies: % 12.75/2.58 | | (40) all_29_2 = 0 % 12.75/2.58 | | (41) ~ (all_29_0 = 0) | ~ (all_29_1 = 0) % 12.75/2.58 | | % 12.75/2.58 | | REDUCE: (18), (40) imply: % 12.75/2.58 | | (42) least(all_29_3, all_25_1, all_27_0) = 0 % 12.75/2.58 | | % 12.75/2.58 | | GROUND_INST: instantiating (3) with all_25_1, all_27_0, all_29_3, % 12.75/2.58 | | simplifying with (9), (13), (16), (42) gives: % 12.75/2.58 | | (43) member(all_29_3, all_27_0) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = % 12.75/2.58 | | 0 | ~ (apply(all_25_1, all_29_3, v0) = v1) | ~ $i(v0) | ? [v2: % 12.75/2.58 | | int] : ( ~ (v2 = 0) & member(v0, all_27_0) = v2)) % 12.75/2.58 | | % 12.75/2.58 | | ALPHA: (43) implies: % 12.75/2.58 | | (44) member(all_29_3, all_27_0) = 0 % 12.75/2.58 | | (45) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, all_29_3, % 12.75/2.58 | | v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 12.75/2.58 | | member(v0, all_27_0) = v2)) % 12.75/2.58 | | % 12.75/2.58 | | GROUND_INST: instantiating (7) with all_29_1, 0, all_27_0, all_29_3, % 12.75/2.58 | | simplifying with (17), (44) gives: % 12.75/2.58 | | (46) all_29_1 = 0 % 12.75/2.58 | | % 12.75/2.58 | | BETA: splitting (41) gives: % 12.75/2.58 | | % 12.75/2.58 | | Case 1: % 12.75/2.58 | | | % 12.75/2.58 | | | (47) ~ (all_29_0 = 0) % 12.75/2.58 | | | % 12.75/2.58 | | | BETA: splitting (22) gives: % 12.75/2.58 | | | % 12.75/2.58 | | | Case 1: % 12.75/2.58 | | | | % 12.75/2.58 | | | | (48) all_29_0 = 0 % 12.75/2.58 | | | | % 12.75/2.58 | | | | REDUCE: (47), (48) imply: % 12.75/2.58 | | | | (49) $false % 12.75/2.58 | | | | % 12.75/2.58 | | | | CLOSE: (49) is inconsistent. % 12.75/2.58 | | | | % 12.75/2.58 | | | Case 2: % 12.75/2.58 | | | | % 12.75/2.58 | | | | (50) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0, % 12.75/2.58 | | | | all_25_1, all_27_0) = 0 & apply(all_25_1, v0, all_29_3) = v1 % 12.75/2.58 | | | | & member(v0, all_25_0) = 0 & $i(v0)) | ? [v0: any] : ? [v1: % 12.75/2.58 | | | | any] : (lower_bound(all_29_3, all_25_1, all_27_0) = v1 & % 12.75/2.58 | | | | member(all_29_3, all_27_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.75/2.58 | | | | % 12.75/2.58 | | | | BETA: splitting (50) gives: % 12.75/2.58 | | | | % 12.75/2.58 | | | | Case 1: % 12.75/2.58 | | | | | % 12.75/2.58 | | | | | (51) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & lower_bound(v0, % 12.75/2.58 | | | | | all_25_1, all_27_0) = 0 & apply(all_25_1, v0, all_29_3) = % 12.75/2.58 | | | | | v1 & member(v0, all_25_0) = 0 & $i(v0)) % 12.75/2.58 | | | | | % 12.75/2.58 | | | | | DELTA: instantiating (51) with fresh symbols all_77_0, all_77_1 gives: % 12.75/2.58 | | | | | (52) ~ (all_77_0 = 0) & lower_bound(all_77_1, all_25_1, all_27_0) % 12.75/2.58 | | | | | = 0 & apply(all_25_1, all_77_1, all_29_3) = all_77_0 & % 12.75/2.58 | | | | | member(all_77_1, all_25_0) = 0 & $i(all_77_1) % 12.75/2.58 | | | | | % 12.75/2.58 | | | | | ALPHA: (52) implies: % 12.75/2.58 | | | | | (53) ~ (all_77_0 = 0) % 12.75/2.58 | | | | | (54) $i(all_77_1) % 12.75/2.58 | | | | | (55) apply(all_25_1, all_77_1, all_29_3) = all_77_0 % 12.75/2.58 | | | | | (56) lower_bound(all_77_1, all_25_1, all_27_0) = 0 % 12.75/2.58 | | | | | % 12.75/2.58 | | | | | GROUND_INST: instantiating (1) with all_25_1, all_27_0, all_77_1, % 12.75/2.58 | | | | | simplifying with (9), (13), (54), (56) gives: % 12.75/2.58 | | | | | (57) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, % 12.75/2.58 | | | | | all_77_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 12.75/2.58 | | | | | = 0) & member(v0, all_27_0) = v2)) % 12.75/2.58 | | | | | % 12.75/2.58 | | | | | GROUND_INST: instantiating (57) with all_29_3, all_77_0, simplifying % 12.75/2.58 | | | | | with (16), (55) gives: % 12.75/2.59 | | | | | (58) all_77_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, % 12.75/2.59 | | | | | all_27_0) = v0) % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | BETA: splitting (58) gives: % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | Case 1: % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | (59) all_77_0 = 0 % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | REDUCE: (53), (59) imply: % 12.75/2.59 | | | | | | (60) $false % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | CLOSE: (60) is inconsistent. % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | Case 2: % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_3, all_27_0) = % 12.75/2.59 | | | | | | v0) % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | DELTA: instantiating (61) with fresh symbol all_89_0 gives: % 12.75/2.59 | | | | | | (62) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0 % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | REF_CLOSE: (7), (44), (62) are inconsistent by sub-proof #1. % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | End of split % 12.75/2.59 | | | | | % 12.75/2.59 | | | | Case 2: % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | (63) ? [v0: any] : ? [v1: any] : (lower_bound(all_29_3, all_25_1, % 12.75/2.59 | | | | | all_27_0) = v1 & member(all_29_3, all_27_0) = v0 & ( ~ (v1 % 12.75/2.59 | | | | | = 0) | ~ (v0 = 0))) % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | DELTA: instantiating (63) with fresh symbols all_77_0, all_77_1 gives: % 12.75/2.59 | | | | | (64) lower_bound(all_29_3, all_25_1, all_27_0) = all_77_0 & % 12.75/2.59 | | | | | member(all_29_3, all_27_0) = all_77_1 & ( ~ (all_77_0 = 0) | % 12.75/2.59 | | | | | ~ (all_77_1 = 0)) % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | ALPHA: (64) implies: % 12.75/2.59 | | | | | (65) member(all_29_3, all_27_0) = all_77_1 % 12.75/2.59 | | | | | (66) lower_bound(all_29_3, all_25_1, all_27_0) = all_77_0 % 12.75/2.59 | | | | | (67) ~ (all_77_0 = 0) | ~ (all_77_1 = 0) % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | GROUND_INST: instantiating (7) with 0, all_77_1, all_27_0, all_29_3, % 12.75/2.59 | | | | | simplifying with (44), (65) gives: % 12.75/2.59 | | | | | (68) all_77_1 = 0 % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | BETA: splitting (67) gives: % 12.75/2.59 | | | | | % 12.75/2.59 | | | | | Case 1: % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | (69) ~ (all_77_0 = 0) % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_3, % 12.75/2.59 | | | | | | all_77_0, simplifying with (9), (13), (16), (66) gives: % 12.75/2.59 | | | | | | (70) all_77_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.75/2.59 | | | | | | apply(all_25_1, all_29_3, v0) = v1 & member(v0, all_27_0) % 12.75/2.59 | | | | | | = 0 & $i(v0)) % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | BETA: splitting (70) gives: % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | Case 1: % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | (71) all_77_0 = 0 % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | REDUCE: (69), (71) imply: % 12.75/2.59 | | | | | | | (72) $false % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | CLOSE: (72) is inconsistent. % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | Case 2: % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | (73) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.75/2.59 | | | | | | | apply(all_25_1, all_29_3, v0) = v1 & member(v0, % 12.75/2.59 | | | | | | | all_27_0) = 0 & $i(v0)) % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | DELTA: instantiating (73) with fresh symbols all_94_0, all_94_1 % 12.75/2.59 | | | | | | | gives: % 12.75/2.59 | | | | | | | (74) ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) = % 12.75/2.59 | | | | | | | all_94_0 & member(all_94_1, all_27_0) = 0 & $i(all_94_1) % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | | REF_CLOSE: (7), (45), (74) are inconsistent by sub-proof #2. % 12.75/2.59 | | | | | | | % 12.75/2.59 | | | | | | End of split % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | Case 2: % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | (75) ~ (all_77_1 = 0) % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | REDUCE: (68), (75) imply: % 12.75/2.59 | | | | | | (76) $false % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | | CLOSE: (76) is inconsistent. % 12.75/2.59 | | | | | | % 12.75/2.59 | | | | | End of split % 12.75/2.59 | | | | | % 12.75/2.59 | | | | End of split % 12.75/2.59 | | | | % 12.75/2.59 | | | End of split % 12.75/2.59 | | | % 12.75/2.59 | | Case 2: % 12.75/2.59 | | | % 12.75/2.59 | | | (77) ~ (all_29_1 = 0) % 12.75/2.59 | | | % 12.75/2.59 | | | REDUCE: (46), (77) imply: % 12.75/2.59 | | | (78) $false % 12.75/2.59 | | | % 12.75/2.59 | | | CLOSE: (78) is inconsistent. % 12.75/2.59 | | | % 12.75/2.59 | | End of split % 12.75/2.59 | | % 12.75/2.59 | End of split % 12.75/2.59 | % 12.75/2.59 End of proof % 12.75/2.59 % 12.75/2.59 Sub-proof #1 shows that the following formulas are inconsistent: % 12.75/2.59 ---------------------------------------------------------------- % 12.75/2.59 (1) ~ (all_89_0 = 0) & member(all_29_3, all_27_0) = all_89_0 % 12.75/2.59 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.75/2.59 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 12.75/2.59 v0)) % 12.75/2.59 (3) member(all_29_3, all_27_0) = 0 % 12.75/2.59 % 12.75/2.59 Begin of proof % 12.75/2.59 | % 12.75/2.59 | ALPHA: (1) implies: % 12.75/2.59 | (4) ~ (all_89_0 = 0) % 12.75/2.59 | (5) member(all_29_3, all_27_0) = all_89_0 % 12.75/2.59 | % 12.75/2.60 | GROUND_INST: instantiating (2) with 0, all_89_0, all_27_0, all_29_3, % 12.75/2.60 | simplifying with (3), (5) gives: % 12.75/2.60 | (6) all_89_0 = 0 % 12.75/2.60 | % 12.75/2.60 | REDUCE: (4), (6) imply: % 12.75/2.60 | (7) $false % 12.75/2.60 | % 12.75/2.60 | CLOSE: (7) is inconsistent. % 12.75/2.60 | % 12.75/2.60 End of proof % 12.75/2.60 % 12.75/2.60 Sub-proof #2 shows that the following formulas are inconsistent: % 12.75/2.60 ---------------------------------------------------------------- % 12.75/2.60 (1) ~ (all_94_0 = 0) & apply(all_25_1, all_29_3, all_94_1) = all_94_0 & % 12.75/2.60 member(all_94_1, all_27_0) = 0 & $i(all_94_1) % 12.75/2.60 (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, all_29_3, v0) % 12.75/2.60 = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 12.75/2.60 all_27_0) = v2)) % 12.75/2.60 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.75/2.60 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 12.75/2.60 v0)) % 12.75/2.60 % 12.75/2.60 Begin of proof % 12.75/2.60 | % 12.75/2.60 | ALPHA: (1) implies: % 12.75/2.60 | (4) ~ (all_94_0 = 0) % 12.75/2.60 | (5) $i(all_94_1) % 12.75/2.60 | (6) member(all_94_1, all_27_0) = 0 % 12.75/2.60 | (7) apply(all_25_1, all_29_3, all_94_1) = all_94_0 % 12.75/2.60 | % 12.75/2.60 | GROUND_INST: instantiating (2) with all_94_1, all_94_0, simplifying with (5), % 12.75/2.60 | (7) gives: % 12.75/2.60 | (8) all_94_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0) % 12.75/2.60 | = v0) % 12.75/2.60 | % 12.75/2.60 | BETA: splitting (8) gives: % 12.75/2.60 | % 12.75/2.60 | Case 1: % 12.75/2.60 | | % 12.75/2.60 | | (9) all_94_0 = 0 % 12.75/2.60 | | % 12.75/2.60 | | REDUCE: (4), (9) imply: % 12.75/2.60 | | (10) $false % 12.75/2.60 | | % 12.75/2.60 | | CLOSE: (10) is inconsistent. % 12.75/2.60 | | % 12.75/2.60 | Case 2: % 12.75/2.60 | | % 12.75/2.60 | | (11) ? [v0: int] : ( ~ (v0 = 0) & member(all_94_1, all_27_0) = v0) % 12.75/2.60 | | % 12.75/2.60 | | DELTA: instantiating (11) with fresh symbol all_106_0 gives: % 12.75/2.60 | | (12) ~ (all_106_0 = 0) & member(all_94_1, all_27_0) = all_106_0 % 12.75/2.60 | | % 12.75/2.60 | | ALPHA: (12) implies: % 12.75/2.60 | | (13) ~ (all_106_0 = 0) % 12.75/2.60 | | (14) member(all_94_1, all_27_0) = all_106_0 % 12.75/2.60 | | % 12.75/2.60 | | GROUND_INST: instantiating (3) with 0, all_106_0, all_27_0, all_94_1, % 12.75/2.60 | | simplifying with (6), (14) gives: % 12.75/2.60 | | (15) all_106_0 = 0 % 12.75/2.60 | | % 12.75/2.60 | | REDUCE: (13), (15) imply: % 12.75/2.60 | | (16) $false % 12.75/2.60 | | % 12.75/2.60 | | CLOSE: (16) is inconsistent. % 12.75/2.60 | | % 12.75/2.60 | End of split % 12.75/2.60 | % 12.75/2.60 End of proof % 12.75/2.60 % SZS output end Proof for theBenchmark % 12.75/2.60 % 12.75/2.60 1991ms %------------------------------------------------------------------------------