%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET774+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.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 15:26:23 EDT 2023 % Result : Theorem 10.37s 2.24s % Output : Proof 13.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET774+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n001.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.34 % CPULimit : 300 % 0.11/0.34 % WCLimit : 300 % 0.11/0.34 % DateTime : Sat Aug 26 12:26:45 EDT 2023 % 0.11/0.34 % CPUTime : % 0.17/0.62 ________ _____ % 0.17/0.62 ___ __ \_________(_)________________________________ % 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.62 % 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.62 (2023-06-19) % 0.17/0.62 % 0.17/0.62 (c) Philipp Rümmer, 2009-2023 % 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.62 Amanda Stjerna. % 0.17/0.62 Free software under BSD-3-Clause. % 0.17/0.62 % 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.62 % 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.17 Prover 4: Preprocessing ... % 3.08/1.17 Prover 1: Preprocessing ... % 3.08/1.22 Prover 3: Preprocessing ... % 3.08/1.22 Prover 6: Preprocessing ... % 3.08/1.22 Prover 2: Preprocessing ... % 3.08/1.22 Prover 5: Preprocessing ... % 3.08/1.22 Prover 0: Preprocessing ... % 8.21/1.93 Prover 5: Proving ... % 8.21/1.94 Prover 2: Proving ... % 8.21/1.94 Prover 6: Proving ... % 9.00/2.01 Prover 3: Constructing countermodel ... % 9.21/2.03 Prover 1: Constructing countermodel ... % 10.37/2.20 Prover 4: Constructing countermodel ... % 10.37/2.24 Prover 3: proved (1599ms) % 10.37/2.24 % 10.37/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.37/2.24 % 10.37/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.37/2.25 Prover 2: stopped % 10.37/2.25 Prover 6: stopped % 10.97/2.30 Prover 5: stopped % 10.97/2.30 Prover 0: Proving ... % 10.97/2.30 Prover 0: stopped % 10.97/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.97/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.97/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.97/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.97/2.36 Prover 8: Preprocessing ... % 10.97/2.37 Prover 7: Preprocessing ... % 10.97/2.37 Prover 11: Preprocessing ... % 10.97/2.38 Prover 13: Preprocessing ... % 10.97/2.39 Prover 10: Preprocessing ... % 10.97/2.46 Prover 1: Found proof (size 51) % 10.97/2.46 Prover 1: proved (1821ms) % 10.97/2.47 Prover 4: stopped % 11.33/2.47 Prover 13: stopped % 11.33/2.48 Prover 10: stopped % 12.28/2.52 Prover 7: Warning: ignoring some quantifiers % 12.28/2.53 Prover 11: stopped % 12.28/2.54 Prover 7: Constructing countermodel ... % 12.28/2.55 Prover 7: stopped % 12.99/2.62 Prover 8: Warning: ignoring some quantifiers % 12.99/2.63 Prover 8: Constructing countermodel ... % 12.99/2.65 Prover 8: stopped % 12.99/2.65 % 12.99/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.99/2.65 % 12.99/2.66 % SZS output start Proof for theBenchmark % 12.99/2.67 Assumptions after simplification: % 12.99/2.67 --------------------------------- % 12.99/2.67 % 12.99/2.67 (pre_order) % 13.45/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, v1) = % 13.45/2.72 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 13.45/2.72 [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 & % 13.45/2.72 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & % 13.45/2.72 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: % 13.45/2.72 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & % 13.45/2.72 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~ % 13.45/2.72 $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] % 13.45/2.72 : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ % 13.45/2.72 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 13.45/2.72 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 13.45/2.72 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) % 13.45/2.72 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : (v3 = % 13.45/2.72 0 | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 13.45/2.72 0) & member(v2, v1) = v4)))) % 13.45/2.72 % 13.45/2.72 (subset) % 13.45/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.45/2.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 13.45/2.72 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 13.45/2.72 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 13.45/2.72 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 13.45/2.72 % 13.45/2.72 (thIII10) % 13.45/2.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 13.45/2.72 pre_order(v2, v1) = v3 & pre_order(v2, v0) = 0 & subset(v1, v0) = 0 & $i(v2) % 13.45/2.72 & $i(v1) & $i(v0)) % 13.45/2.72 % 13.45/2.72 (function-axioms) % 13.45/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.45/2.73 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, % 13.45/2.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.45/2.73 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = % 13.45/2.73 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.45/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.45/2.73 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0: % 13.45/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.45/2.73 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & % 13.45/2.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.45/2.73 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 13.45/2.73 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.45/2.73 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 13.45/2.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.45/2.73 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.45/2.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.45/2.73 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 13.45/2.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 13.45/2.73 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.45/2.73 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 13.45/2.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.45/2.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 13.45/2.73 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.45/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 13.45/2.73 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.45/2.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.45/2.73 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 13.45/2.73 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 13.45/2.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 13.45/2.73 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.45/2.73 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 13.45/2.73 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 13.45/2.73 (power_set(v2) = v0)) % 13.45/2.73 % 13.45/2.73 Further assumptions not needed in the proof: % 13.45/2.73 -------------------------------------------- % 13.45/2.73 difference, disjoint, empty_set, equal_set, equivalence, equivalence_class, % 13.45/2.73 intersection, partition, power_set, product, singleton, sum, union, % 13.45/2.73 unordered_pair % 13.45/2.73 % 13.45/2.73 Those formulas are unsatisfiable: % 13.45/2.73 --------------------------------- % 13.45/2.73 % 13.45/2.73 Begin of proof % 13.45/2.73 | % 13.45/2.73 | ALPHA: (subset) implies: % 13.45/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 13.45/2.73 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 13.45/2.73 | member(v2, v1) = 0)) % 13.45/2.73 | % 13.45/2.73 | ALPHA: (pre_order) implies: % 13.45/2.74 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~ $i(v1) | % 13.45/2.74 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 13.45/2.74 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) % 13.45/2.74 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] % 13.45/2.74 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & % 13.45/2.74 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 % 13.45/2.74 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & % 13.45/2.74 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | % 13.45/2.74 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 13.45/2.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, % 13.45/2.74 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 13.45/2.74 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & % 13.45/2.74 | apply(v0, v3, v5) = v6 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 % 13.45/2.74 | & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v5) & $i(v4) & % 13.45/2.74 | $i(v3)) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, v3, % 13.45/2.74 | v3) = v4 & member(v3, v1) = 0 & $i(v3))) % 13.45/2.74 | % 13.45/2.74 | ALPHA: (function-axioms) implies: % 13.45/2.74 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.45/2.74 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 13.45/2.74 | = v0)) % 13.45/2.74 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.45/2.74 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 13.45/2.74 | (apply(v4, v3, v2) = v0)) % 13.45/2.74 | % 13.45/2.74 | DELTA: instantiating (thIII10) with fresh symbols all_20_0, all_20_1, % 13.45/2.74 | all_20_2, all_20_3 gives: % 13.45/2.74 | (6) ~ (all_20_0 = 0) & pre_order(all_20_1, all_20_2) = all_20_0 & % 13.45/2.74 | pre_order(all_20_1, all_20_3) = 0 & subset(all_20_2, all_20_3) = 0 & % 13.45/2.74 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) % 13.45/2.74 | % 13.45/2.74 | ALPHA: (6) implies: % 13.45/2.74 | (7) ~ (all_20_0 = 0) % 13.45/2.74 | (8) $i(all_20_3) % 13.45/2.74 | (9) $i(all_20_2) % 13.45/2.74 | (10) $i(all_20_1) % 13.45/2.74 | (11) subset(all_20_2, all_20_3) = 0 % 13.45/2.74 | (12) pre_order(all_20_1, all_20_3) = 0 % 13.45/2.74 | (13) pre_order(all_20_1, all_20_2) = all_20_0 % 13.45/2.74 | % 13.45/2.74 | GROUND_INST: instantiating (1) with all_20_2, all_20_3, simplifying with (8), % 13.45/2.74 | (9), (11) gives: % 13.45/2.74 | (14) ! [v0: $i] : ( ~ (member(v0, all_20_2) = 0) | ~ $i(v0) | member(v0, % 13.45/2.74 | all_20_3) = 0) % 13.45/2.74 | % 13.45/2.74 | GROUND_INST: instantiating (2) with all_20_1, all_20_3, simplifying with (8), % 13.45/2.74 | (10), (12) gives: % 13.45/2.75 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.45/2.75 | (apply(all_20_1, v0, v2) = v3) | ~ (apply(all_20_1, v0, v1) = 0) | % 13.45/2.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 13.45/2.75 | [v6: any] : ? [v7: any] : (apply(all_20_1, v1, v2) = v7 & % 13.45/2.75 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0, % 13.45/2.75 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 13.45/2.75 | (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 13.45/2.75 | (apply(all_20_1, v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 13.45/2.75 | = 0) & member(v0, all_20_3) = v2)) % 13.45/2.75 | % 13.45/2.75 | ALPHA: (15) implies: % 13.45/2.75 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_20_1, v0, v0) = % 13.45/2.75 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 13.45/2.75 | all_20_3) = v2)) % 13.45/2.75 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.45/2.75 | (apply(all_20_1, v0, v2) = v3) | ~ (apply(all_20_1, v0, v1) = 0) | % 13.45/2.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 13.45/2.75 | [v6: any] : ? [v7: any] : (apply(all_20_1, v1, v2) = v7 & % 13.45/2.75 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0, % 13.45/2.75 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 13.45/2.75 | (v4 = 0)))) % 13.45/2.75 | % 13.45/2.75 | GROUND_INST: instantiating (3) with all_20_1, all_20_2, all_20_0, simplifying % 13.45/2.75 | with (9), (10), (13) gives: % 13.45/2.75 | (18) all_20_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 13.45/2.75 | : ( ~ (v3 = 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2) % 13.45/2.75 | = v3 & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 & % 13.45/2.75 | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) & % 13.45/2.75 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 13.45/2.75 | apply(all_20_1, v0, v0) = v1 & member(v0, all_20_2) = 0 & $i(v0)) % 13.45/2.75 | % 13.45/2.75 | BETA: splitting (18) gives: % 13.45/2.75 | % 13.45/2.75 | Case 1: % 13.45/2.75 | | % 13.45/2.75 | | (19) all_20_0 = 0 % 13.45/2.75 | | % 13.45/2.75 | | REDUCE: (7), (19) imply: % 13.45/2.76 | | (20) $false % 13.45/2.76 | | % 13.45/2.76 | | CLOSE: (20) is inconsistent. % 13.45/2.76 | | % 13.45/2.76 | Case 2: % 13.45/2.76 | | % 13.45/2.76 | | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 13.45/2.76 | | 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2) = v3 % 13.45/2.76 | | & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 & % 13.45/2.76 | | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) & % 13.45/2.76 | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 13.45/2.76 | | apply(all_20_1, v0, v0) = v1 & member(v0, all_20_2) = 0 & $i(v0)) % 13.45/2.76 | | % 13.45/2.76 | | BETA: splitting (21) gives: % 13.45/2.76 | | % 13.45/2.76 | | Case 1: % 13.45/2.76 | | | % 13.45/2.76 | | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 13.45/2.76 | | | 0) & apply(all_20_1, v1, v2) = 0 & apply(all_20_1, v0, v2) = % 13.45/2.76 | | | v3 & apply(all_20_1, v0, v1) = 0 & member(v2, all_20_2) = 0 & % 13.45/2.76 | | | member(v1, all_20_2) = 0 & member(v0, all_20_2) = 0 & $i(v2) & % 13.45/2.76 | | | $i(v1) & $i(v0)) % 13.45/2.76 | | | % 13.45/2.76 | | | DELTA: instantiating (22) with fresh symbols all_40_0, all_40_1, all_40_2, % 13.45/2.76 | | | all_40_3 gives: % 13.45/2.76 | | | (23) ~ (all_40_0 = 0) & apply(all_20_1, all_40_2, all_40_1) = 0 & % 13.45/2.76 | | | apply(all_20_1, all_40_3, all_40_1) = all_40_0 & apply(all_20_1, % 13.45/2.76 | | | all_40_3, all_40_2) = 0 & member(all_40_1, all_20_2) = 0 & % 13.45/2.76 | | | member(all_40_2, all_20_2) = 0 & member(all_40_3, all_20_2) = 0 & % 13.45/2.76 | | | $i(all_40_1) & $i(all_40_2) & $i(all_40_3) % 13.45/2.76 | | | % 13.45/2.76 | | | ALPHA: (23) implies: % 13.45/2.76 | | | (24) ~ (all_40_0 = 0) % 13.45/2.76 | | | (25) $i(all_40_3) % 13.45/2.76 | | | (26) $i(all_40_2) % 13.45/2.76 | | | (27) $i(all_40_1) % 13.45/2.76 | | | (28) member(all_40_3, all_20_2) = 0 % 13.45/2.76 | | | (29) member(all_40_2, all_20_2) = 0 % 13.45/2.76 | | | (30) member(all_40_1, all_20_2) = 0 % 13.45/2.76 | | | (31) apply(all_20_1, all_40_3, all_40_2) = 0 % 13.45/2.77 | | | (32) apply(all_20_1, all_40_3, all_40_1) = all_40_0 % 13.45/2.77 | | | (33) apply(all_20_1, all_40_2, all_40_1) = 0 % 13.45/2.77 | | | % 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_3, simplifying with (25), (28) % 13.45/2.77 | | | gives: % 13.45/2.77 | | | (34) member(all_40_3, all_20_3) = 0 % 13.45/2.77 | | | % 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_2, simplifying with (26), (29) % 13.45/2.77 | | | gives: % 13.45/2.77 | | | (35) member(all_40_2, all_20_3) = 0 % 13.45/2.77 | | | % 13.45/2.77 | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (27), (30) % 13.45/2.77 | | | gives: % 13.45/2.77 | | | (36) member(all_40_1, all_20_3) = 0 % 13.45/2.77 | | | % 13.45/2.77 | | | GROUND_INST: instantiating (17) with all_40_3, all_40_2, all_40_1, % 13.45/2.77 | | | all_40_0, simplifying with (25), (26), (27), (31), (32) % 13.45/2.77 | | | gives: % 13.45/2.77 | | | (37) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 13.45/2.77 | | | [v3: any] : (apply(all_20_1, all_40_2, all_40_1) = v3 & % 13.45/2.77 | | | member(all_40_1, all_20_3) = v2 & member(all_40_2, all_20_3) = % 13.45/2.77 | | | v1 & member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = % 13.45/2.77 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 13.45/2.77 | | | % 13.45/2.77 | | | BETA: splitting (37) gives: % 13.45/2.77 | | | % 13.45/2.77 | | | Case 1: % 13.45/2.77 | | | | % 13.45/2.77 | | | | (38) all_40_0 = 0 % 13.45/2.77 | | | | % 13.45/2.77 | | | | REDUCE: (24), (38) imply: % 13.45/2.77 | | | | (39) $false % 13.45/2.77 | | | | % 13.45/2.77 | | | | CLOSE: (39) is inconsistent. % 13.45/2.77 | | | | % 13.45/2.77 | | | Case 2: % 13.45/2.77 | | | | % 13.45/2.77 | | | | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.45/2.77 | | | | (apply(all_20_1, all_40_2, all_40_1) = v3 & member(all_40_1, % 13.45/2.77 | | | | all_20_3) = v2 & member(all_40_2, all_20_3) = v1 & % 13.45/2.77 | | | | member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 13.45/2.77 | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 13.45/2.77 | | | | % 13.45/2.77 | | | | DELTA: instantiating (40) with fresh symbols all_52_0, all_52_1, % 13.45/2.77 | | | | all_52_2, all_52_3 gives: % 13.45/2.77 | | | | (41) apply(all_20_1, all_40_2, all_40_1) = all_52_0 & % 13.45/2.77 | | | | member(all_40_1, all_20_3) = all_52_1 & member(all_40_2, % 13.45/2.77 | | | | all_20_3) = all_52_2 & member(all_40_3, all_20_3) = all_52_3 & % 13.45/2.77 | | | | ( ~ (all_52_0 = 0) | ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~ % 13.45/2.77 | | | | (all_52_3 = 0)) % 13.45/2.77 | | | | % 13.45/2.77 | | | | ALPHA: (41) implies: % 13.45/2.77 | | | | (42) member(all_40_3, all_20_3) = all_52_3 % 13.45/2.77 | | | | (43) member(all_40_2, all_20_3) = all_52_2 % 13.45/2.77 | | | | (44) member(all_40_1, all_20_3) = all_52_1 % 13.45/2.78 | | | | (45) apply(all_20_1, all_40_2, all_40_1) = all_52_0 % 13.45/2.78 | | | | (46) ~ (all_52_0 = 0) | ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~ % 13.45/2.78 | | | | (all_52_3 = 0) % 13.45/2.78 | | | | % 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_3, all_20_3, all_40_3, % 13.45/2.78 | | | | simplifying with (34), (42) gives: % 13.45/2.78 | | | | (47) all_52_3 = 0 % 13.45/2.78 | | | | % 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_2, all_20_3, all_40_2, % 13.45/2.78 | | | | simplifying with (35), (43) gives: % 13.45/2.78 | | | | (48) all_52_2 = 0 % 13.45/2.78 | | | | % 13.45/2.78 | | | | GROUND_INST: instantiating (4) with 0, all_52_1, all_20_3, all_40_1, % 13.45/2.78 | | | | simplifying with (36), (44) gives: % 13.45/2.78 | | | | (49) all_52_1 = 0 % 13.45/2.78 | | | | % 13.45/2.78 | | | | GROUND_INST: instantiating (5) with 0, all_52_0, all_40_1, all_40_2, % 13.45/2.78 | | | | all_20_1, simplifying with (33), (45) gives: % 13.45/2.78 | | | | (50) all_52_0 = 0 % 13.45/2.78 | | | | % 13.45/2.78 | | | | BETA: splitting (46) gives: % 13.45/2.78 | | | | % 13.45/2.78 | | | | Case 1: % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | (51) ~ (all_52_0 = 0) % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | REDUCE: (50), (51) imply: % 13.45/2.78 | | | | | (52) $false % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | CLOSE: (52) is inconsistent. % 13.45/2.78 | | | | | % 13.45/2.78 | | | | Case 2: % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | (53) ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | ~ (all_52_3 = 0) % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | BETA: splitting (53) gives: % 13.45/2.78 | | | | | % 13.45/2.78 | | | | | Case 1: % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | (54) ~ (all_52_1 = 0) % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | REDUCE: (49), (54) imply: % 13.45/2.78 | | | | | | (55) $false % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | CLOSE: (55) is inconsistent. % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | Case 2: % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | (56) ~ (all_52_2 = 0) | ~ (all_52_3 = 0) % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | BETA: splitting (56) gives: % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | | Case 1: % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | (57) ~ (all_52_2 = 0) % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | REDUCE: (48), (57) imply: % 13.45/2.78 | | | | | | | (58) $false % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | CLOSE: (58) is inconsistent. % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | Case 2: % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | (59) ~ (all_52_3 = 0) % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | REDUCE: (47), (59) imply: % 13.45/2.78 | | | | | | | (60) $false % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | | CLOSE: (60) is inconsistent. % 13.45/2.78 | | | | | | | % 13.45/2.78 | | | | | | End of split % 13.45/2.78 | | | | | | % 13.45/2.78 | | | | | End of split % 13.45/2.78 | | | | | % 13.45/2.78 | | | | End of split % 13.45/2.78 | | | | % 13.45/2.78 | | | End of split % 13.45/2.78 | | | % 13.45/2.78 | | Case 2: % 13.45/2.78 | | | % 13.45/2.78 | | | (61) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_20_1, v0, % 13.45/2.78 | | | v0) = v1 & member(v0, all_20_2) = 0 & $i(v0)) % 13.45/2.78 | | | % 13.45/2.78 | | | DELTA: instantiating (61) with fresh symbols all_40_0, all_40_1 gives: % 13.45/2.78 | | | (62) ~ (all_40_0 = 0) & apply(all_20_1, all_40_1, all_40_1) = all_40_0 % 13.45/2.78 | | | & member(all_40_1, all_20_2) = 0 & $i(all_40_1) % 13.45/2.78 | | | % 13.45/2.78 | | | ALPHA: (62) implies: % 13.45/2.78 | | | (63) ~ (all_40_0 = 0) % 13.45/2.79 | | | (64) $i(all_40_1) % 13.45/2.79 | | | (65) member(all_40_1, all_20_2) = 0 % 13.45/2.79 | | | (66) apply(all_20_1, all_40_1, all_40_1) = all_40_0 % 13.45/2.79 | | | % 13.45/2.79 | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (64), (65) % 13.45/2.79 | | | gives: % 13.45/2.79 | | | (67) member(all_40_1, all_20_3) = 0 % 13.45/2.79 | | | % 13.45/2.79 | | | GROUND_INST: instantiating (16) with all_40_1, all_40_0, simplifying with % 13.45/2.79 | | | (64), (66) gives: % 13.45/2.79 | | | (68) all_40_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, % 13.45/2.79 | | | all_20_3) = v0) % 13.45/2.79 | | | % 13.45/2.79 | | | BETA: splitting (68) gives: % 13.45/2.79 | | | % 13.45/2.79 | | | Case 1: % 13.45/2.79 | | | | % 13.45/2.79 | | | | (69) all_40_0 = 0 % 13.45/2.79 | | | | % 13.45/2.79 | | | | REDUCE: (63), (69) imply: % 13.45/2.79 | | | | (70) $false % 13.45/2.79 | | | | % 13.45/2.79 | | | | CLOSE: (70) is inconsistent. % 13.45/2.79 | | | | % 13.45/2.79 | | | Case 2: % 13.45/2.79 | | | | % 13.45/2.79 | | | | (71) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_20_3) = v0) % 13.45/2.79 | | | | % 13.45/2.79 | | | | DELTA: instantiating (71) with fresh symbol all_52_0 gives: % 13.45/2.79 | | | | (72) ~ (all_52_0 = 0) & member(all_40_1, all_20_3) = all_52_0 % 13.45/2.79 | | | | % 13.45/2.79 | | | | ALPHA: (72) implies: % 13.45/2.79 | | | | (73) ~ (all_52_0 = 0) % 13.45/2.79 | | | | (74) member(all_40_1, all_20_3) = all_52_0 % 13.45/2.79 | | | | % 13.45/2.79 | | | | GROUND_INST: instantiating (4) with 0, all_52_0, all_20_3, all_40_1, % 13.45/2.79 | | | | simplifying with (67), (74) gives: % 13.45/2.79 | | | | (75) all_52_0 = 0 % 13.45/2.79 | | | | % 13.45/2.79 | | | | REDUCE: (73), (75) imply: % 13.45/2.79 | | | | (76) $false % 13.85/2.79 | | | | % 13.85/2.79 | | | | CLOSE: (76) is inconsistent. % 13.85/2.79 | | | | % 13.85/2.79 | | | End of split % 13.85/2.79 | | | % 13.85/2.79 | | End of split % 13.85/2.79 | | % 13.85/2.79 | End of split % 13.85/2.79 | % 13.85/2.79 End of proof % 13.85/2.79 % SZS output end Proof for theBenchmark % 13.85/2.79 % 13.85/2.79 2173ms %------------------------------------------------------------------------------