%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET805+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 : n017.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 15:26:31 EDT 2023 % Result : Theorem 9.49s 2.07s % Output : Proof 12.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET805+4 : TPTP v8.1.2. Released v3.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 09:12:41 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.95/1.17 Prover 4: Preprocessing ... % 2.95/1.17 Prover 1: Preprocessing ... % 2.95/1.21 Prover 6: Preprocessing ... % 2.95/1.21 Prover 2: Preprocessing ... % 2.95/1.21 Prover 5: Preprocessing ... % 2.95/1.21 Prover 3: Preprocessing ... % 2.95/1.21 Prover 0: Preprocessing ... % 7.33/1.76 Prover 5: Proving ... % 7.51/1.79 Prover 2: Proving ... % 8.17/1.88 Prover 3: Constructing countermodel ... % 8.17/1.88 Prover 6: Proving ... % 8.17/1.91 Prover 1: Constructing countermodel ... % 8.83/2.04 Prover 0: Proving ... % 9.49/2.04 Prover 4: Constructing countermodel ... % 9.49/2.07 Prover 3: proved (1441ms) % 9.49/2.07 % 9.49/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.49/2.07 % 9.49/2.07 Prover 6: stopped % 9.49/2.07 Prover 5: stopped % 9.49/2.08 Prover 2: stopped % 9.49/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.49/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.49/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.49/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.49/2.09 Prover 0: stopped % 9.49/2.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.96/2.12 Prover 10: Preprocessing ... % 9.96/2.12 Prover 7: Preprocessing ... % 9.96/2.13 Prover 11: Preprocessing ... % 9.96/2.13 Prover 13: Preprocessing ... % 9.96/2.15 Prover 8: Preprocessing ... % 10.36/2.23 Prover 7: Warning: ignoring some quantifiers % 10.36/2.23 Prover 10: Warning: ignoring some quantifiers % 11.01/2.25 Prover 7: Constructing countermodel ... % 11.01/2.27 Prover 10: Constructing countermodel ... % 11.26/2.31 Prover 13: Warning: ignoring some quantifiers % 11.66/2.35 Prover 13: Constructing countermodel ... % 11.66/2.36 Prover 1: Found proof (size 76) % 11.66/2.36 Prover 1: proved (1736ms) % 11.66/2.36 Prover 10: stopped % 11.66/2.36 Prover 7: stopped % 11.66/2.36 Prover 4: stopped % 11.66/2.36 Prover 13: stopped % 11.66/2.37 Prover 8: Warning: ignoring some quantifiers % 11.66/2.38 Prover 8: Constructing countermodel ... % 11.66/2.39 Prover 8: stopped % 12.36/2.46 Prover 11: Constructing countermodel ... % 12.36/2.48 Prover 11: stopped % 12.36/2.48 % 12.36/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.36/2.48 % 12.36/2.49 % SZS output start Proof for theBenchmark % 12.36/2.49 Assumptions after simplification: % 12.36/2.49 --------------------------------- % 12.36/2.50 % 12.36/2.50 (order) % 12.36/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) = v2) | % 12.36/2.55 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 12.36/2.55 int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 & % 12.36/2.55 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & % 12.36/2.55 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] % 12.36/2.55 : ( ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, % 12.36/2.55 v1) = 0 & member(v3, v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: % 12.36/2.55 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & % 12.36/2.55 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) % 12.36/2.55 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 % 12.36/2.55 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ % 12.36/2.55 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 12.36/2.55 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 12.36/2.55 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) % 12.36/2.55 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = % 12.36/2.55 v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : % 12.36/2.55 ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) = % 12.36/2.55 v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 12.36/2.55 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 12.36/2.55 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 12.36/2.55 % 12.36/2.55 (subset) % 12.36/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 12.36/2.55 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 12.36/2.55 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 12.36/2.55 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 12.36/2.55 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 12.36/2.55 % 12.36/2.55 (thIV17) % 12.77/2.55 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 12.77/2.55 : ? [v3: int] : ( ~ (v3 = 0) & order(v0, v2) = v3 & subset(v2, v1) = 0 & % 12.77/2.55 $i(v2))) % 12.77/2.55 % 12.77/2.55 (function-axioms) % 12.77/2.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.77/2.56 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 12.77/2.56 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 12.77/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.77/2.56 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 12.77/2.56 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 12.77/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.77/2.56 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 12.77/2.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.77/2.56 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 12.77/2.56 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.77/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.77/2.56 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 12.77/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.77/2.56 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 12.77/2.56 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.77/2.56 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 12.77/2.56 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 12.77/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.77/2.56 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 12.77/2.56 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.77/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.77/2.56 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 12.77/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.77/2.56 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 12.77/2.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.77/2.56 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 12.77/2.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.77/2.56 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 12.77/2.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.77/2.56 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 12.77/2.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 12.77/2.56 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.77/2.56 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 12.77/2.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.77/2.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 12.77/2.56 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.77/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 12.77/2.56 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.77/2.56 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.77/2.56 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 12.77/2.56 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 12.77/2.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 12.77/2.56 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 12.77/2.56 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 12.77/2.56 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 12.77/2.56 (power_set(v2) = v0)) % 12.77/2.56 % 12.77/2.56 Further assumptions not needed in the proof: % 12.77/2.56 -------------------------------------------- % 12.77/2.56 difference, empty_set, equal_set, greatest, greatest_lower_bound, intersection, % 12.77/2.56 least, least_upper_bound, lower_bound, max, min, power_set, product, singleton, % 12.77/2.56 sum, total_order, union, unordered_pair, upper_bound % 12.77/2.56 % 12.77/2.56 Those formulas are unsatisfiable: % 12.77/2.56 --------------------------------- % 12.77/2.56 % 12.77/2.56 Begin of proof % 12.77/2.56 | % 12.77/2.56 | ALPHA: (subset) implies: % 12.77/2.56 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 12.77/2.56 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 12.77/2.56 | member(v2, v1) = 0)) % 12.77/2.56 | % 12.77/2.56 | ALPHA: (order) implies: % 12.77/2.56 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) | ~ % 12.77/2.56 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 12.77/2.57 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) % 12.77/2.57 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] % 12.77/2.57 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & % 12.77/2.57 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 % 12.77/2.57 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & % 12.77/2.57 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) | % 12.77/2.57 | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 12.77/2.57 | : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) % 12.77/2.57 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: % 12.77/2.57 | $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 12.77/2.57 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 12.77/2.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) % 12.77/2.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.77/2.57 | $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & % 12.77/2.57 | apply(v0, v3, v5) = v6 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 % 12.77/2.57 | & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v5) & $i(v4) & % 12.77/2.57 | $i(v3)) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & apply(v0, v4, % 12.77/2.57 | v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, % 12.77/2.57 | v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 12.77/2.57 | = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) % 12.77/2.57 | % 12.77/2.57 | ALPHA: (function-axioms) implies: % 12.77/2.57 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.77/2.57 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 12.77/2.57 | = v0)) % 12.77/2.57 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.77/2.57 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 12.77/2.57 | (apply(v4, v3, v2) = v0)) % 12.77/2.57 | % 12.77/2.57 | DELTA: instantiating (thIV17) with fresh symbols all_25_0, all_25_1 gives: % 12.77/2.57 | (6) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0: % 12.77/2.57 | $i] : ? [v1: int] : ( ~ (v1 = 0) & order(all_25_1, v0) = v1 & % 12.77/2.57 | subset(v0, all_25_0) = 0 & $i(v0)) % 12.77/2.57 | % 12.77/2.57 | ALPHA: (6) implies: % 12.77/2.57 | (7) $i(all_25_1) % 12.77/2.57 | (8) $i(all_25_0) % 12.77/2.57 | (9) order(all_25_1, all_25_0) = 0 % 12.77/2.57 | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & order(all_25_1, v0) = v1 & % 12.77/2.57 | subset(v0, all_25_0) = 0 & $i(v0)) % 12.77/2.57 | % 12.77/2.57 | DELTA: instantiating (10) with fresh symbols all_27_0, all_27_1 gives: % 12.77/2.57 | (11) ~ (all_27_0 = 0) & order(all_25_1, all_27_1) = all_27_0 & % 12.77/2.57 | subset(all_27_1, all_25_0) = 0 & $i(all_27_1) % 12.77/2.57 | % 12.77/2.57 | ALPHA: (11) implies: % 12.77/2.57 | (12) ~ (all_27_0 = 0) % 12.77/2.57 | (13) $i(all_27_1) % 12.77/2.57 | (14) subset(all_27_1, all_25_0) = 0 % 12.77/2.57 | (15) order(all_25_1, all_27_1) = all_27_0 % 12.77/2.57 | % 12.77/2.57 | GROUND_INST: instantiating (1) with all_27_1, all_25_0, simplifying with (8), % 12.77/2.57 | (13), (14) gives: % 12.77/2.57 | (16) ! [v0: $i] : ( ~ (member(v0, all_27_1) = 0) | ~ $i(v0) | member(v0, % 12.77/2.57 | all_25_0) = 0) % 12.77/2.57 | % 12.77/2.57 | GROUND_INST: instantiating (2) with all_25_1, all_25_0, simplifying with (7), % 12.77/2.57 | (8), (9) gives: % 12.77/2.58 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.77/2.58 | (apply(all_25_1, v0, v2) = v3) | ~ (apply(all_25_1, v0, v1) = 0) | % 12.77/2.58 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 12.77/2.58 | [v6: any] : ? [v7: any] : (apply(all_25_1, v1, v2) = v7 & % 12.77/2.58 | member(v2, all_25_0) = v6 & member(v1, all_25_0) = v5 & member(v0, % 12.77/2.58 | all_25_0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 12.77/2.58 | (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 12.77/2.58 | (apply(all_25_1, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] % 12.77/2.58 | : ? [v3: any] : ? [v4: any] : (apply(all_25_1, v1, v0) = v4 & % 12.77/2.58 | member(v1, all_25_0) = v3 & member(v0, all_25_0) = v2 & ( ~ (v4 = % 12.77/2.58 | 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] % 12.77/2.58 | : (v1 = 0 | ~ (apply(all_25_1, v0, v0) = v1) | ~ $i(v0) | ? [v2: % 12.77/2.58 | int] : ( ~ (v2 = 0) & member(v0, all_25_0) = v2)) % 12.77/2.58 | % 12.77/2.58 | ALPHA: (17) implies: % 12.77/2.58 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0, v0) = % 12.77/2.58 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 12.77/2.58 | all_25_0) = v2)) % 12.77/2.58 | (19) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_25_1, v0, v1) = % 12.77/2.58 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: % 12.77/2.58 | any] : (apply(all_25_1, v1, v0) = v4 & member(v1, all_25_0) = v3 & % 12.77/2.58 | member(v0, all_25_0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = % 12.77/2.58 | 0)))) % 12.77/2.58 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.77/2.58 | (apply(all_25_1, v0, v2) = v3) | ~ (apply(all_25_1, v0, v1) = 0) | % 12.77/2.58 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 12.77/2.58 | [v6: any] : ? [v7: any] : (apply(all_25_1, v1, v2) = v7 & % 12.77/2.58 | member(v2, all_25_0) = v6 & member(v1, all_25_0) = v5 & member(v0, % 12.77/2.58 | all_25_0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 12.77/2.58 | (v4 = 0)))) % 12.77/2.58 | % 12.77/2.58 | GROUND_INST: instantiating (3) with all_25_1, all_27_1, all_27_0, simplifying % 12.77/2.58 | with (7), (13), (15) gives: % 12.77/2.58 | (21) all_27_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 12.77/2.58 | : ( ~ (v3 = 0) & apply(all_25_1, v1, v2) = 0 & apply(all_25_1, v0, v2) % 12.77/2.58 | = v3 & apply(all_25_1, v0, v1) = 0 & member(v2, all_27_1) = 0 & % 12.77/2.58 | member(v1, all_27_1) = 0 & member(v0, all_27_1) = 0 & $i(v2) & % 12.77/2.58 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 12.77/2.58 | apply(all_25_1, v1, v0) = 0 & apply(all_25_1, v0, v1) = 0 & % 12.77/2.58 | member(v1, all_27_1) = 0 & member(v0, all_27_1) = 0 & $i(v1) & % 12.77/2.58 | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.77/2.58 | apply(all_25_1, v0, v0) = v1 & member(v0, all_27_1) = 0 & $i(v0)) % 12.77/2.58 | % 12.77/2.58 | BETA: splitting (21) gives: % 12.77/2.58 | % 12.77/2.58 | Case 1: % 12.77/2.58 | | % 12.77/2.58 | | (22) all_27_0 = 0 % 12.77/2.58 | | % 12.77/2.58 | | REDUCE: (12), (22) imply: % 12.77/2.58 | | (23) $false % 12.77/2.58 | | % 12.77/2.58 | | CLOSE: (23) is inconsistent. % 12.77/2.58 | | % 12.77/2.58 | Case 2: % 12.77/2.58 | | % 12.77/2.59 | | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 12.77/2.59 | | 0) & apply(all_25_1, v1, v2) = 0 & apply(all_25_1, v0, v2) = v3 % 12.77/2.59 | | & apply(all_25_1, v0, v1) = 0 & member(v2, all_27_1) = 0 & % 12.77/2.59 | | member(v1, all_27_1) = 0 & member(v0, all_27_1) = 0 & $i(v2) & % 12.77/2.59 | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 12.77/2.59 | | apply(all_25_1, v1, v0) = 0 & apply(all_25_1, v0, v1) = 0 & % 12.77/2.59 | | member(v1, all_27_1) = 0 & member(v0, all_27_1) = 0 & $i(v1) & % 12.77/2.59 | | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.77/2.59 | | apply(all_25_1, v0, v0) = v1 & member(v0, all_27_1) = 0 & $i(v0)) % 12.77/2.59 | | % 12.77/2.59 | | BETA: splitting (24) gives: % 12.77/2.59 | | % 12.77/2.59 | | Case 1: % 12.77/2.59 | | | % 12.77/2.59 | | | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 12.77/2.59 | | | 0) & apply(all_25_1, v1, v2) = 0 & apply(all_25_1, v0, v2) = % 12.77/2.59 | | | v3 & apply(all_25_1, v0, v1) = 0 & member(v2, all_27_1) = 0 & % 12.77/2.59 | | | member(v1, all_27_1) = 0 & member(v0, all_27_1) = 0 & $i(v2) & % 12.77/2.59 | | | $i(v1) & $i(v0)) % 12.77/2.59 | | | % 12.77/2.59 | | | DELTA: instantiating (25) with fresh symbols all_47_0, all_47_1, all_47_2, % 12.77/2.59 | | | all_47_3 gives: % 12.77/2.59 | | | (26) ~ (all_47_0 = 0) & apply(all_25_1, all_47_2, all_47_1) = 0 & % 12.77/2.59 | | | apply(all_25_1, all_47_3, all_47_1) = all_47_0 & apply(all_25_1, % 12.77/2.59 | | | all_47_3, all_47_2) = 0 & member(all_47_1, all_27_1) = 0 & % 12.77/2.59 | | | member(all_47_2, all_27_1) = 0 & member(all_47_3, all_27_1) = 0 & % 12.77/2.59 | | | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) % 12.77/2.59 | | | % 12.77/2.59 | | | ALPHA: (26) implies: % 12.77/2.59 | | | (27) ~ (all_47_0 = 0) % 12.77/2.59 | | | (28) $i(all_47_3) % 12.77/2.59 | | | (29) $i(all_47_2) % 12.77/2.59 | | | (30) $i(all_47_1) % 12.77/2.59 | | | (31) member(all_47_3, all_27_1) = 0 % 12.77/2.59 | | | (32) member(all_47_2, all_27_1) = 0 % 12.77/2.59 | | | (33) member(all_47_1, all_27_1) = 0 % 12.77/2.59 | | | (34) apply(all_25_1, all_47_3, all_47_2) = 0 % 12.77/2.59 | | | (35) apply(all_25_1, all_47_3, all_47_1) = all_47_0 % 12.77/2.59 | | | (36) apply(all_25_1, all_47_2, all_47_1) = 0 % 12.77/2.59 | | | % 12.77/2.59 | | | GROUND_INST: instantiating (16) with all_47_3, simplifying with (28), (31) % 12.77/2.59 | | | gives: % 12.77/2.59 | | | (37) member(all_47_3, all_25_0) = 0 % 12.77/2.59 | | | % 12.77/2.59 | | | GROUND_INST: instantiating (16) with all_47_2, simplifying with (29), (32) % 12.77/2.59 | | | gives: % 12.77/2.59 | | | (38) member(all_47_2, all_25_0) = 0 % 12.77/2.59 | | | % 12.77/2.59 | | | GROUND_INST: instantiating (16) with all_47_1, simplifying with (30), (33) % 12.77/2.59 | | | gives: % 12.77/2.59 | | | (39) member(all_47_1, all_25_0) = 0 % 12.77/2.59 | | | % 12.77/2.59 | | | GROUND_INST: instantiating (20) with all_47_3, all_47_2, all_47_1, % 12.77/2.59 | | | all_47_0, simplifying with (28), (29), (30), (34), (35) % 12.77/2.59 | | | gives: % 12.77/2.59 | | | (40) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 12.77/2.59 | | | [v3: any] : (apply(all_25_1, all_47_2, all_47_1) = v3 & % 12.77/2.59 | | | member(all_47_1, all_25_0) = v2 & member(all_47_2, all_25_0) = % 12.77/2.59 | | | v1 & member(all_47_3, all_25_0) = v0 & ( ~ (v3 = 0) | ~ (v2 = % 12.77/2.59 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 12.77/2.59 | | | % 12.77/2.59 | | | BETA: splitting (40) gives: % 12.77/2.59 | | | % 12.77/2.59 | | | Case 1: % 12.77/2.59 | | | | % 12.77/2.59 | | | | (41) all_47_0 = 0 % 12.77/2.59 | | | | % 12.77/2.59 | | | | REDUCE: (27), (41) imply: % 12.77/2.59 | | | | (42) $false % 12.77/2.59 | | | | % 12.77/2.59 | | | | CLOSE: (42) is inconsistent. % 12.77/2.59 | | | | % 12.77/2.59 | | | Case 2: % 12.77/2.59 | | | | % 12.77/2.59 | | | | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 12.77/2.59 | | | | (apply(all_25_1, all_47_2, all_47_1) = v3 & member(all_47_1, % 12.77/2.59 | | | | all_25_0) = v2 & member(all_47_2, all_25_0) = v1 & % 12.77/2.59 | | | | member(all_47_3, all_25_0) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 12.77/2.59 | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 12.77/2.59 | | | | % 12.77/2.59 | | | | DELTA: instantiating (43) with fresh symbols all_59_0, all_59_1, % 12.77/2.59 | | | | all_59_2, all_59_3 gives: % 12.77/2.59 | | | | (44) apply(all_25_1, all_47_2, all_47_1) = all_59_0 & % 12.77/2.59 | | | | member(all_47_1, all_25_0) = all_59_1 & member(all_47_2, % 12.77/2.59 | | | | all_25_0) = all_59_2 & member(all_47_3, all_25_0) = all_59_3 & % 12.77/2.59 | | | | ( ~ (all_59_0 = 0) | ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | ~ % 12.77/2.59 | | | | (all_59_3 = 0)) % 12.77/2.59 | | | | % 12.77/2.59 | | | | ALPHA: (44) implies: % 12.77/2.60 | | | | (45) member(all_47_3, all_25_0) = all_59_3 % 12.77/2.60 | | | | (46) member(all_47_2, all_25_0) = all_59_2 % 12.77/2.60 | | | | (47) member(all_47_1, all_25_0) = all_59_1 % 12.77/2.60 | | | | (48) apply(all_25_1, all_47_2, all_47_1) = all_59_0 % 12.77/2.60 | | | | (49) ~ (all_59_0 = 0) | ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | ~ % 12.77/2.60 | | | | (all_59_3 = 0) % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (4) with 0, all_59_3, all_25_0, all_47_3, % 12.77/2.60 | | | | simplifying with (37), (45) gives: % 12.77/2.60 | | | | (50) all_59_3 = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (4) with 0, all_59_2, all_25_0, all_47_2, % 12.77/2.60 | | | | simplifying with (38), (46) gives: % 12.77/2.60 | | | | (51) all_59_2 = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (4) with 0, all_59_1, all_25_0, all_47_1, % 12.77/2.60 | | | | simplifying with (39), (47) gives: % 12.77/2.60 | | | | (52) all_59_1 = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (5) with 0, all_59_0, all_47_1, all_47_2, % 12.77/2.60 | | | | all_25_1, simplifying with (36), (48) gives: % 12.77/2.60 | | | | (53) all_59_0 = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | BETA: splitting (49) gives: % 12.77/2.60 | | | | % 12.77/2.60 | | | | Case 1: % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | (54) ~ (all_59_0 = 0) % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | REDUCE: (53), (54) imply: % 12.77/2.60 | | | | | (55) $false % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | CLOSE: (55) is inconsistent. % 12.77/2.60 | | | | | % 12.77/2.60 | | | | Case 2: % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | (56) ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | ~ (all_59_3 = 0) % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | BETA: splitting (56) gives: % 12.77/2.60 | | | | | % 12.77/2.60 | | | | | Case 1: % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | (57) ~ (all_59_1 = 0) % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | REDUCE: (52), (57) imply: % 12.77/2.60 | | | | | | (58) $false % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | CLOSE: (58) is inconsistent. % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | Case 2: % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | (59) ~ (all_59_2 = 0) | ~ (all_59_3 = 0) % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | BETA: splitting (59) gives: % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | | Case 1: % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | (60) ~ (all_59_2 = 0) % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | REDUCE: (51), (60) imply: % 12.77/2.60 | | | | | | | (61) $false % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | CLOSE: (61) is inconsistent. % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | Case 2: % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | (62) ~ (all_59_3 = 0) % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | REDUCE: (50), (62) imply: % 12.77/2.60 | | | | | | | (63) $false % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | | CLOSE: (63) is inconsistent. % 12.77/2.60 | | | | | | | % 12.77/2.60 | | | | | | End of split % 12.77/2.60 | | | | | | % 12.77/2.60 | | | | | End of split % 12.77/2.60 | | | | | % 12.77/2.60 | | | | End of split % 12.77/2.60 | | | | % 12.77/2.60 | | | End of split % 12.77/2.60 | | | % 12.77/2.60 | | Case 2: % 12.77/2.60 | | | % 12.77/2.60 | | | (64) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & apply(all_25_1, v1, % 12.77/2.60 | | | v0) = 0 & apply(all_25_1, v0, v1) = 0 & member(v1, all_27_1) = % 12.77/2.60 | | | 0 & member(v0, all_27_1) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 12.77/2.60 | | | ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, v0, v0) = v1 & % 12.77/2.60 | | | member(v0, all_27_1) = 0 & $i(v0)) % 12.77/2.60 | | | % 12.77/2.60 | | | BETA: splitting (64) gives: % 12.77/2.60 | | | % 12.77/2.60 | | | Case 1: % 12.77/2.60 | | | | % 12.77/2.60 | | | | (65) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & apply(all_25_1, v1, % 12.77/2.60 | | | | v0) = 0 & apply(all_25_1, v0, v1) = 0 & member(v1, all_27_1) % 12.77/2.60 | | | | = 0 & member(v0, all_27_1) = 0 & $i(v1) & $i(v0)) % 12.77/2.60 | | | | % 12.77/2.60 | | | | DELTA: instantiating (65) with fresh symbols all_47_0, all_47_1 gives: % 12.77/2.60 | | | | (66) ~ (all_47_0 = all_47_1) & apply(all_25_1, all_47_0, all_47_1) = % 12.77/2.60 | | | | 0 & apply(all_25_1, all_47_1, all_47_0) = 0 & member(all_47_0, % 12.77/2.60 | | | | all_27_1) = 0 & member(all_47_1, all_27_1) = 0 & $i(all_47_0) % 12.77/2.60 | | | | & $i(all_47_1) % 12.77/2.60 | | | | % 12.77/2.60 | | | | ALPHA: (66) implies: % 12.77/2.60 | | | | (67) ~ (all_47_0 = all_47_1) % 12.77/2.60 | | | | (68) $i(all_47_1) % 12.77/2.60 | | | | (69) $i(all_47_0) % 12.77/2.60 | | | | (70) member(all_47_1, all_27_1) = 0 % 12.77/2.60 | | | | (71) member(all_47_0, all_27_1) = 0 % 12.77/2.60 | | | | (72) apply(all_25_1, all_47_1, all_47_0) = 0 % 12.77/2.60 | | | | (73) apply(all_25_1, all_47_0, all_47_1) = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (16) with all_47_1, simplifying with (68), % 12.77/2.60 | | | | (70) gives: % 12.77/2.60 | | | | (74) member(all_47_1, all_25_0) = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (16) with all_47_0, simplifying with (69), % 12.77/2.60 | | | | (71) gives: % 12.77/2.60 | | | | (75) member(all_47_0, all_25_0) = 0 % 12.77/2.60 | | | | % 12.77/2.60 | | | | GROUND_INST: instantiating (19) with all_47_0, all_47_1, simplifying % 12.77/2.60 | | | | with (68), (69), (73) gives: % 12.77/2.61 | | | | (76) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 12.77/2.61 | | | | : (apply(all_25_1, all_47_1, all_47_0) = v2 & member(all_47_0, % 12.77/2.61 | | | | all_25_0) = v0 & member(all_47_1, all_25_0) = v1 & ( ~ (v2 = % 12.77/2.61 | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 12.77/2.61 | | | | % 12.77/2.61 | | | | BETA: splitting (76) gives: % 12.77/2.61 | | | | % 12.77/2.61 | | | | Case 1: % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | (77) all_47_0 = all_47_1 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | REDUCE: (67), (77) imply: % 12.77/2.61 | | | | | (78) $false % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | CLOSE: (78) is inconsistent. % 12.77/2.61 | | | | | % 12.77/2.61 | | | | Case 2: % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_25_1, % 12.77/2.61 | | | | | all_47_1, all_47_0) = v2 & member(all_47_0, all_25_0) = v0 % 12.77/2.61 | | | | | & member(all_47_1, all_25_0) = v1 & ( ~ (v2 = 0) | ~ (v1 = % 12.77/2.61 | | | | | 0) | ~ (v0 = 0))) % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | DELTA: instantiating (79) with fresh symbols all_59_0, all_59_1, % 12.77/2.61 | | | | | all_59_2 gives: % 12.77/2.61 | | | | | (80) apply(all_25_1, all_47_1, all_47_0) = all_59_0 & % 12.77/2.61 | | | | | member(all_47_0, all_25_0) = all_59_2 & member(all_47_1, % 12.77/2.61 | | | | | all_25_0) = all_59_1 & ( ~ (all_59_0 = 0) | ~ (all_59_1 = % 12.77/2.61 | | | | | 0) | ~ (all_59_2 = 0)) % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | ALPHA: (80) implies: % 12.77/2.61 | | | | | (81) member(all_47_1, all_25_0) = all_59_1 % 12.77/2.61 | | | | | (82) member(all_47_0, all_25_0) = all_59_2 % 12.77/2.61 | | | | | (83) apply(all_25_1, all_47_1, all_47_0) = all_59_0 % 12.77/2.61 | | | | | (84) ~ (all_59_0 = 0) | ~ (all_59_1 = 0) | ~ (all_59_2 = 0) % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | GROUND_INST: instantiating (4) with 0, all_59_1, all_25_0, all_47_1, % 12.77/2.61 | | | | | simplifying with (74), (81) gives: % 12.77/2.61 | | | | | (85) all_59_1 = 0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | GROUND_INST: instantiating (4) with 0, all_59_2, all_25_0, all_47_0, % 12.77/2.61 | | | | | simplifying with (75), (82) gives: % 12.77/2.61 | | | | | (86) all_59_2 = 0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | GROUND_INST: instantiating (5) with 0, all_59_0, all_47_0, all_47_1, % 12.77/2.61 | | | | | all_25_1, simplifying with (72), (83) gives: % 12.77/2.61 | | | | | (87) all_59_0 = 0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | BETA: splitting (84) gives: % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | Case 1: % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | (88) ~ (all_59_0 = 0) % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | REDUCE: (87), (88) imply: % 12.77/2.61 | | | | | | (89) $false % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | CLOSE: (89) is inconsistent. % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | Case 2: % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | (90) ~ (all_59_1 = 0) | ~ (all_59_2 = 0) % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | BETA: splitting (90) gives: % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | | Case 1: % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | (91) ~ (all_59_1 = 0) % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | REDUCE: (85), (91) imply: % 12.77/2.61 | | | | | | | (92) $false % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | CLOSE: (92) is inconsistent. % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | Case 2: % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | (93) ~ (all_59_2 = 0) % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | REDUCE: (86), (93) imply: % 12.77/2.61 | | | | | | | (94) $false % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | | CLOSE: (94) is inconsistent. % 12.77/2.61 | | | | | | | % 12.77/2.61 | | | | | | End of split % 12.77/2.61 | | | | | | % 12.77/2.61 | | | | | End of split % 12.77/2.61 | | | | | % 12.77/2.61 | | | | End of split % 12.77/2.61 | | | | % 12.77/2.61 | | | Case 2: % 12.77/2.61 | | | | % 12.77/2.61 | | | | (95) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_1, v0, % 12.77/2.61 | | | | v0) = v1 & member(v0, all_27_1) = 0 & $i(v0)) % 12.77/2.61 | | | | % 12.77/2.61 | | | | DELTA: instantiating (95) with fresh symbols all_47_0, all_47_1 gives: % 12.77/2.61 | | | | (96) ~ (all_47_0 = 0) & apply(all_25_1, all_47_1, all_47_1) = % 12.77/2.61 | | | | all_47_0 & member(all_47_1, all_27_1) = 0 & $i(all_47_1) % 12.77/2.61 | | | | % 12.77/2.61 | | | | ALPHA: (96) implies: % 12.77/2.61 | | | | (97) ~ (all_47_0 = 0) % 12.77/2.61 | | | | (98) $i(all_47_1) % 12.77/2.61 | | | | (99) member(all_47_1, all_27_1) = 0 % 12.77/2.61 | | | | (100) apply(all_25_1, all_47_1, all_47_1) = all_47_0 % 12.77/2.61 | | | | % 12.77/2.61 | | | | GROUND_INST: instantiating (16) with all_47_1, simplifying with (98), % 12.77/2.61 | | | | (99) gives: % 12.77/2.61 | | | | (101) member(all_47_1, all_25_0) = 0 % 12.77/2.61 | | | | % 12.77/2.61 | | | | GROUND_INST: instantiating (18) with all_47_1, all_47_0, simplifying % 12.77/2.61 | | | | with (98), (100) gives: % 12.77/2.61 | | | | (102) all_47_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_47_1, % 12.77/2.61 | | | | all_25_0) = v0) % 12.77/2.61 | | | | % 12.77/2.61 | | | | BETA: splitting (102) gives: % 12.77/2.61 | | | | % 12.77/2.61 | | | | Case 1: % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | (103) all_47_0 = 0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | REDUCE: (97), (103) imply: % 12.77/2.61 | | | | | (104) $false % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | CLOSE: (104) is inconsistent. % 12.77/2.61 | | | | | % 12.77/2.61 | | | | Case 2: % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | (105) ? [v0: int] : ( ~ (v0 = 0) & member(all_47_1, all_25_0) = % 12.77/2.61 | | | | | v0) % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | DELTA: instantiating (105) with fresh symbol all_59_0 gives: % 12.77/2.61 | | | | | (106) ~ (all_59_0 = 0) & member(all_47_1, all_25_0) = all_59_0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | ALPHA: (106) implies: % 12.77/2.61 | | | | | (107) ~ (all_59_0 = 0) % 12.77/2.61 | | | | | (108) member(all_47_1, all_25_0) = all_59_0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | GROUND_INST: instantiating (4) with 0, all_59_0, all_25_0, all_47_1, % 12.77/2.61 | | | | | simplifying with (101), (108) gives: % 12.77/2.61 | | | | | (109) all_59_0 = 0 % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | REDUCE: (107), (109) imply: % 12.77/2.61 | | | | | (110) $false % 12.77/2.61 | | | | | % 12.77/2.61 | | | | | CLOSE: (110) is inconsistent. % 12.77/2.61 | | | | | % 12.77/2.61 | | | | End of split % 12.77/2.62 | | | | % 12.77/2.62 | | | End of split % 12.77/2.62 | | | % 12.77/2.62 | | End of split % 12.77/2.62 | | % 12.77/2.62 | End of split % 12.77/2.62 | % 12.77/2.62 End of proof % 12.77/2.62 % SZS output end Proof for theBenchmark % 12.77/2.62 % 12.77/2.62 2013ms %------------------------------------------------------------------------------