%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET795+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 : n028.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 15:26:28 EDT 2023 % Result : Theorem 10.26s 2.09s % Output : Proof 12.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET795+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 11:10:22 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.67/1.09 Prover 4: Preprocessing ... % 2.67/1.09 Prover 1: Preprocessing ... % 3.20/1.13 Prover 5: Preprocessing ... % 3.20/1.13 Prover 6: Preprocessing ... % 3.20/1.13 Prover 2: Preprocessing ... % 3.20/1.13 Prover 3: Preprocessing ... % 3.20/1.14 Prover 0: Preprocessing ... % 6.19/1.62 Prover 5: Proving ... % 7.17/1.65 Prover 2: Proving ... % 7.63/1.76 Prover 6: Proving ... % 8.05/1.79 Prover 1: Constructing countermodel ... % 8.05/1.79 Prover 3: Constructing countermodel ... % 9.30/1.97 Prover 4: Constructing countermodel ... % 9.79/2.04 Prover 0: Proving ... % 10.26/2.09 Prover 3: proved (1456ms) % 10.26/2.09 % 10.26/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.26/2.09 % 10.26/2.09 Prover 5: stopped % 10.26/2.09 Prover 6: stopped % 10.26/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.26/2.10 Prover 0: stopped % 10.26/2.10 Prover 2: stopped % 10.26/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.26/2.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.26/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.26/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.26/2.13 Prover 7: Preprocessing ... % 10.26/2.15 Prover 8: Preprocessing ... % 10.26/2.16 Prover 11: Preprocessing ... % 10.26/2.16 Prover 10: Preprocessing ... % 10.26/2.16 Prover 13: Preprocessing ... % 10.26/2.23 Prover 7: Warning: ignoring some quantifiers % 10.26/2.24 Prover 10: Warning: ignoring some quantifiers % 10.26/2.25 Prover 1: Found proof (size 58) % 10.26/2.25 Prover 1: proved (1628ms) % 10.26/2.25 Prover 4: stopped % 10.26/2.25 Prover 11: stopped % 10.26/2.25 Prover 7: Constructing countermodel ... % 10.26/2.25 Prover 10: Constructing countermodel ... % 10.26/2.27 Prover 10: stopped % 10.26/2.27 Prover 7: stopped % 10.26/2.29 Prover 13: Warning: ignoring some quantifiers % 11.71/2.30 Prover 13: Constructing countermodel ... % 11.71/2.31 Prover 13: stopped % 12.17/2.34 Prover 8: Warning: ignoring some quantifiers % 12.17/2.35 Prover 8: Constructing countermodel ... % 12.17/2.36 Prover 8: stopped % 12.17/2.36 % 12.17/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.17/2.36 % 12.17/2.36 % SZS output start Proof for theBenchmark % 12.17/2.37 Assumptions after simplification: % 12.17/2.37 --------------------------------- % 12.17/2.37 % 12.17/2.37 (least_upper_bound) % 12.38/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.38/2.40 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 12.38/2.40 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 12.38/2.40 upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v6 & member(v5, v3) = 0 % 12.38/2.40 & $i(v5)) | ? [v5: any] : ? [v6: any] : (upper_bound(v0, v2, v1) = v6 & % 12.38/2.40 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 12.38/2.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (least_upper_bound(v0, v1, v2, v3) % 12.38/2.40 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (upper_bound(v0, % 12.38/2.40 v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~ (upper_bound(v4, % 12.38/2.40 v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (apply(v2, % 12.38/2.40 v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))))) % 12.38/2.40 % 12.38/2.40 (order) % 12.38/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) = v2) | % 12.38/2.41 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 12.38/2.41 int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 & % 12.38/2.41 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & % 12.38/2.41 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] % 12.38/2.41 : ( ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, % 12.38/2.41 v1) = 0 & member(v3, v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: % 12.38/2.41 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & % 12.38/2.41 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) % 12.38/2.41 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 % 12.38/2.41 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ % 12.38/2.41 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 12.38/2.41 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 12.38/2.41 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) % 12.38/2.41 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = % 12.38/2.41 v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : % 12.38/2.41 ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) = % 12.38/2.41 v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 12.38/2.41 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 12.38/2.41 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 12.38/2.41 % 12.38/2.41 (thIV7) % 12.38/2.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.38/2.41 int] : ( ~ (v5 = 0) & least_upper_bound(v3, v4, v0, v1) = v5 & order(v0, v1) % 12.38/2.41 = 0 & apply(v0, v2, v3) = 0 & unordered_pair(v2, v3) = v4 & member(v3, v1) = % 12.38/2.41 0 & member(v2, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.38/2.41 % 12.38/2.41 (unordered_pair) % 12.38/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.38/2.41 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | % 12.38/2.41 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : ! % 12.38/2.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~ % 12.38/2.41 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 12.38/2.41 $i(v1) | ~ $i(v0)) % 12.38/2.41 % 12.38/2.41 (upper_bound) % 12.38/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.38/2.41 (upper_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 12.38/2.41 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, % 12.38/2.41 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.38/2.41 (upper_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: % 12.38/2.41 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | % 12.38/2.41 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 12.38/2.41 % 12.38/2.41 (function-axioms) % 12.38/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.38/2.42 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 12.38/2.42 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 12.38/2.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.38/2.42 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 12.38/2.42 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 12.38/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.38/2.42 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 12.38/2.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.38/2.42 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 12.38/2.42 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.38/2.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.38/2.42 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 12.38/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.38/2.42 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 12.38/2.42 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.38/2.42 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 12.38/2.42 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 12.38/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.38/2.42 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 12.38/2.42 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.38/2.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 12.38/2.42 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 12.38/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.38/2.42 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 12.38/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.38/2.42 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 12.38/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.38/2.42 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 12.38/2.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.38/2.42 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 12.38/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 12.38/2.42 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.38/2.42 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 12.38/2.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.38/2.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 12.38/2.42 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.38/2.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 12.38/2.42 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.38/2.42 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.38/2.42 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 12.38/2.42 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 12.38/2.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 12.38/2.42 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 12.38/2.42 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 12.38/2.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 12.38/2.42 (power_set(v2) = v0)) % 12.38/2.42 % 12.38/2.42 Further assumptions not needed in the proof: % 12.38/2.42 -------------------------------------------- % 12.38/2.42 difference, empty_set, equal_set, greatest, greatest_lower_bound, intersection, % 12.38/2.42 least, lower_bound, max, min, power_set, product, singleton, subset, sum, % 12.38/2.42 total_order, union % 12.38/2.42 % 12.38/2.42 Those formulas are unsatisfiable: % 12.38/2.42 --------------------------------- % 12.38/2.42 % 12.38/2.42 Begin of proof % 12.38/2.42 | % 12.38/2.42 | ALPHA: (unordered_pair) implies: % 12.38/2.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 12.38/2.43 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 12.38/2.43 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 12.38/2.43 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.38/2.43 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 12.38/2.43 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) % 12.38/2.43 | % 12.38/2.43 | ALPHA: (order) implies: % 12.38/2.43 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) | ~ % 12.38/2.43 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 12.38/2.43 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) % 12.38/2.43 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] % 12.38/2.43 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & % 12.38/2.43 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 % 12.38/2.43 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & % 12.38/2.43 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) | % 12.38/2.43 | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 12.38/2.43 | : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) % 12.38/2.43 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: % 12.38/2.43 | $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 12.38/2.43 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 12.38/2.43 | % 12.38/2.43 | ALPHA: (upper_bound) implies: % 12.38/2.43 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (upper_bound(v2, v0, v1) % 12.38/2.43 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: % 12.38/2.43 | int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5: % 12.38/2.43 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 12.38/2.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.38/2.43 | (upper_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.38/2.43 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & % 12.38/2.43 | member(v4, v1) = 0 & $i(v4))) % 12.38/2.43 | % 12.38/2.43 | ALPHA: (least_upper_bound) implies: % 12.38/2.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.38/2.43 | (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ % 12.38/2.43 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 % 12.38/2.43 | = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v6 & % 12.38/2.43 | member(v5, v3) = 0 & $i(v5)) | ? [v5: any] : ? [v6: any] : % 12.38/2.43 | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | % 12.38/2.43 | ~ (v5 = 0)))) % 12.38/2.43 | % 12.38/2.43 | ALPHA: (function-axioms) implies: % 12.38/2.43 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.38/2.43 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 12.38/2.43 | = v0)) % 12.38/2.43 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.38/2.43 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 12.38/2.43 | (apply(v4, v3, v2) = v0)) % 12.38/2.43 | % 12.38/2.44 | DELTA: instantiating (thIV7) with fresh symbols all_25_0, all_25_1, all_25_2, % 12.38/2.44 | all_25_3, all_25_4, all_25_5 gives: % 12.38/2.44 | (9) ~ (all_25_0 = 0) & least_upper_bound(all_25_2, all_25_1, all_25_5, % 12.38/2.44 | all_25_4) = all_25_0 & order(all_25_5, all_25_4) = 0 & % 12.38/2.44 | apply(all_25_5, all_25_3, all_25_2) = 0 & unordered_pair(all_25_3, % 12.38/2.44 | all_25_2) = all_25_1 & member(all_25_2, all_25_4) = 0 & % 12.38/2.44 | member(all_25_3, all_25_4) = 0 & $i(all_25_1) & $i(all_25_2) & % 12.38/2.44 | $i(all_25_3) & $i(all_25_4) & $i(all_25_5) % 12.38/2.44 | % 12.38/2.44 | ALPHA: (9) implies: % 12.38/2.44 | (10) ~ (all_25_0 = 0) % 12.38/2.44 | (11) $i(all_25_5) % 12.38/2.44 | (12) $i(all_25_4) % 12.38/2.44 | (13) $i(all_25_3) % 12.38/2.44 | (14) $i(all_25_2) % 12.38/2.44 | (15) $i(all_25_1) % 12.68/2.44 | (16) member(all_25_2, all_25_4) = 0 % 12.68/2.44 | (17) unordered_pair(all_25_3, all_25_2) = all_25_1 % 12.68/2.44 | (18) apply(all_25_5, all_25_3, all_25_2) = 0 % 12.68/2.44 | (19) order(all_25_5, all_25_4) = 0 % 12.68/2.44 | (20) least_upper_bound(all_25_2, all_25_1, all_25_5, all_25_4) = all_25_0 % 12.68/2.44 | % 12.68/2.44 | GROUND_INST: instantiating (3) with all_25_5, all_25_4, simplifying with (11), % 12.68/2.44 | (12), (19) gives: % 12.68/2.44 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.68/2.44 | (apply(all_25_5, v0, v2) = v3) | ~ (apply(all_25_5, v0, v1) = 0) | % 12.68/2.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 12.68/2.44 | [v6: any] : ? [v7: any] : (apply(all_25_5, v1, v2) = v7 & % 12.68/2.44 | member(v2, all_25_4) = v6 & member(v1, all_25_4) = v5 & member(v0, % 12.68/2.44 | all_25_4) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 12.68/2.44 | (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 12.68/2.44 | (apply(all_25_5, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] % 12.68/2.44 | : ? [v3: any] : ? [v4: any] : (apply(all_25_5, v1, v0) = v4 & % 12.68/2.44 | member(v1, all_25_4) = v3 & member(v0, all_25_4) = v2 & ( ~ (v4 = % 12.68/2.44 | 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] % 12.68/2.44 | : (v1 = 0 | ~ (apply(all_25_5, v0, v0) = v1) | ~ $i(v0) | ? [v2: % 12.68/2.44 | int] : ( ~ (v2 = 0) & member(v0, all_25_4) = v2)) % 12.68/2.44 | % 12.68/2.44 | ALPHA: (21) implies: % 12.68/2.44 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_5, v0, v0) = % 12.68/2.44 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 12.68/2.44 | all_25_4) = v2)) % 12.68/2.44 | % 12.68/2.44 | GROUND_INST: instantiating (6) with all_25_2, all_25_1, all_25_5, all_25_4, % 12.68/2.44 | all_25_0, simplifying with (11), (12), (14), (15), (20) gives: % 12.68/2.45 | (23) all_25_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.68/2.45 | upper_bound(v0, all_25_5, all_25_1) = 0 & apply(all_25_5, all_25_2, % 12.68/2.45 | v0) = v1 & member(v0, all_25_4) = 0 & $i(v0)) | ? [v0: any] : ? % 12.68/2.45 | [v1: any] : (upper_bound(all_25_2, all_25_5, all_25_1) = v1 & % 12.68/2.45 | member(all_25_2, all_25_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.68/2.45 | % 12.68/2.45 | BETA: splitting (23) gives: % 12.68/2.45 | % 12.68/2.45 | Case 1: % 12.68/2.45 | | % 12.68/2.45 | | (24) all_25_0 = 0 % 12.68/2.45 | | % 12.68/2.45 | | REDUCE: (10), (24) imply: % 12.68/2.45 | | (25) $false % 12.68/2.45 | | % 12.68/2.45 | | CLOSE: (25) is inconsistent. % 12.68/2.45 | | % 12.68/2.45 | Case 2: % 12.68/2.45 | | % 12.68/2.45 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & upper_bound(v0, % 12.68/2.45 | | all_25_5, all_25_1) = 0 & apply(all_25_5, all_25_2, v0) = v1 & % 12.68/2.45 | | member(v0, all_25_4) = 0 & $i(v0)) | ? [v0: any] : ? [v1: any] : % 12.68/2.45 | | (upper_bound(all_25_2, all_25_5, all_25_1) = v1 & member(all_25_2, % 12.68/2.45 | | all_25_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.68/2.45 | | % 12.68/2.45 | | BETA: splitting (26) gives: % 12.68/2.45 | | % 12.68/2.45 | | Case 1: % 12.68/2.45 | | | % 12.68/2.45 | | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & upper_bound(v0, % 12.68/2.45 | | | all_25_5, all_25_1) = 0 & apply(all_25_5, all_25_2, v0) = v1 & % 12.68/2.45 | | | member(v0, all_25_4) = 0 & $i(v0)) % 12.68/2.45 | | | % 12.68/2.45 | | | DELTA: instantiating (27) with fresh symbols all_43_0, all_43_1 gives: % 12.68/2.45 | | | (28) ~ (all_43_0 = 0) & upper_bound(all_43_1, all_25_5, all_25_1) = 0 % 12.68/2.45 | | | & apply(all_25_5, all_25_2, all_43_1) = all_43_0 & % 12.68/2.45 | | | member(all_43_1, all_25_4) = 0 & $i(all_43_1) % 12.68/2.45 | | | % 12.68/2.45 | | | ALPHA: (28) implies: % 12.68/2.45 | | | (29) ~ (all_43_0 = 0) % 12.68/2.45 | | | (30) $i(all_43_1) % 12.68/2.45 | | | (31) apply(all_25_5, all_25_2, all_43_1) = all_43_0 % 12.68/2.45 | | | (32) upper_bound(all_43_1, all_25_5, all_25_1) = 0 % 12.68/2.45 | | | % 12.68/2.45 | | | GROUND_INST: instantiating (4) with all_25_5, all_25_1, all_43_1, % 12.68/2.45 | | | simplifying with (11), (15), (30), (32) gives: % 12.68/2.45 | | | (33) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_5, v0, % 12.68/2.45 | | | all_43_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 12.68/2.45 | | | member(v0, all_25_1) = v2)) % 12.68/2.45 | | | % 12.68/2.45 | | | GROUND_INST: instantiating (33) with all_25_2, all_43_0, simplifying with % 12.68/2.45 | | | (14), (31) gives: % 12.68/2.45 | | | (34) all_43_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_25_2, % 12.68/2.45 | | | all_25_1) = v0) % 12.68/2.45 | | | % 12.68/2.45 | | | BETA: splitting (34) gives: % 12.68/2.45 | | | % 12.68/2.45 | | | Case 1: % 12.68/2.45 | | | | % 12.68/2.45 | | | | (35) all_43_0 = 0 % 12.68/2.45 | | | | % 12.68/2.45 | | | | REDUCE: (29), (35) imply: % 12.68/2.45 | | | | (36) $false % 12.68/2.45 | | | | % 12.68/2.45 | | | | CLOSE: (36) is inconsistent. % 12.68/2.45 | | | | % 12.68/2.45 | | | Case 2: % 12.68/2.45 | | | | % 12.68/2.45 | | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_25_2, all_25_1) = v0) % 12.68/2.45 | | | | % 12.68/2.45 | | | | DELTA: instantiating (37) with fresh symbol all_61_0 gives: % 12.68/2.45 | | | | (38) ~ (all_61_0 = 0) & member(all_25_2, all_25_1) = all_61_0 % 12.68/2.45 | | | | % 12.68/2.45 | | | | ALPHA: (38) implies: % 12.68/2.46 | | | | (39) ~ (all_61_0 = 0) % 12.68/2.46 | | | | (40) member(all_25_2, all_25_1) = all_61_0 % 12.68/2.46 | | | | % 12.68/2.46 | | | | GROUND_INST: instantiating (2) with all_25_2, all_25_3, all_25_2, % 12.68/2.46 | | | | all_25_1, all_61_0, simplifying with (13), (14), (17), (40) % 12.68/2.46 | | | | gives: % 12.68/2.46 | | | | (41) all_61_0 = 0 % 12.68/2.46 | | | | % 12.68/2.46 | | | | REDUCE: (39), (41) imply: % 12.68/2.46 | | | | (42) $false % 12.68/2.46 | | | | % 12.68/2.46 | | | | CLOSE: (42) is inconsistent. % 12.68/2.46 | | | | % 12.68/2.46 | | | End of split % 12.68/2.46 | | | % 12.68/2.46 | | Case 2: % 12.68/2.46 | | | % 12.68/2.46 | | | (43) ? [v0: any] : ? [v1: any] : (upper_bound(all_25_2, all_25_5, % 12.68/2.46 | | | all_25_1) = v1 & member(all_25_2, all_25_1) = v0 & ( ~ (v1 = % 12.68/2.46 | | | 0) | ~ (v0 = 0))) % 12.68/2.46 | | | % 12.68/2.46 | | | DELTA: instantiating (43) with fresh symbols all_43_0, all_43_1 gives: % 12.68/2.46 | | | (44) upper_bound(all_25_2, all_25_5, all_25_1) = all_43_0 & % 12.68/2.46 | | | member(all_25_2, all_25_1) = all_43_1 & ( ~ (all_43_0 = 0) | ~ % 12.68/2.46 | | | (all_43_1 = 0)) % 12.68/2.46 | | | % 12.68/2.46 | | | ALPHA: (44) implies: % 12.68/2.46 | | | (45) member(all_25_2, all_25_1) = all_43_1 % 12.68/2.46 | | | (46) upper_bound(all_25_2, all_25_5, all_25_1) = all_43_0 % 12.78/2.46 | | | (47) ~ (all_43_0 = 0) | ~ (all_43_1 = 0) % 12.78/2.46 | | | % 12.78/2.46 | | | GROUND_INST: instantiating (2) with all_25_2, all_25_3, all_25_2, % 12.78/2.46 | | | all_25_1, all_43_1, simplifying with (13), (14), (17), (45) % 12.78/2.46 | | | gives: % 12.78/2.46 | | | (48) all_43_1 = 0 % 12.78/2.46 | | | % 12.78/2.46 | | | GROUND_INST: instantiating (5) with all_25_5, all_25_1, all_25_2, % 12.78/2.46 | | | all_43_0, simplifying with (11), (14), (15), (46) gives: % 12.78/2.46 | | | (49) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.78/2.46 | | | apply(all_25_5, v0, all_25_2) = v1 & member(v0, all_25_1) = 0 & % 12.78/2.46 | | | $i(v0)) % 12.78/2.46 | | | % 12.78/2.46 | | | BETA: splitting (47) gives: % 12.78/2.46 | | | % 12.78/2.46 | | | Case 1: % 12.78/2.46 | | | | % 12.78/2.46 | | | | (50) ~ (all_43_0 = 0) % 12.78/2.46 | | | | % 12.78/2.46 | | | | BETA: splitting (49) gives: % 12.78/2.46 | | | | % 12.78/2.46 | | | | Case 1: % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | (51) all_43_0 = 0 % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | REDUCE: (50), (51) imply: % 12.78/2.46 | | | | | (52) $false % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | CLOSE: (52) is inconsistent. % 12.78/2.46 | | | | | % 12.78/2.46 | | | | Case 2: % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | (53) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_25_5, % 12.78/2.46 | | | | | v0, all_25_2) = v1 & member(v0, all_25_1) = 0 & $i(v0)) % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | DELTA: instantiating (53) with fresh symbols all_59_0, all_59_1 gives: % 12.78/2.46 | | | | | (54) ~ (all_59_0 = 0) & apply(all_25_5, all_59_1, all_25_2) = % 12.78/2.46 | | | | | all_59_0 & member(all_59_1, all_25_1) = 0 & $i(all_59_1) % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | ALPHA: (54) implies: % 12.78/2.46 | | | | | (55) ~ (all_59_0 = 0) % 12.78/2.46 | | | | | (56) $i(all_59_1) % 12.78/2.46 | | | | | (57) member(all_59_1, all_25_1) = 0 % 12.78/2.46 | | | | | (58) apply(all_25_5, all_59_1, all_25_2) = all_59_0 % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | GROUND_INST: instantiating (1) with all_59_1, all_25_3, all_25_2, % 12.78/2.46 | | | | | all_25_1, simplifying with (13), (14), (17), (56), (57) % 12.78/2.46 | | | | | gives: % 12.78/2.46 | | | | | (59) all_59_1 = all_25_2 | all_59_1 = all_25_3 % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | BETA: splitting (59) gives: % 12.78/2.46 | | | | | % 12.78/2.46 | | | | | Case 1: % 12.78/2.46 | | | | | | % 12.78/2.46 | | | | | | (60) all_59_1 = all_25_2 % 12.78/2.46 | | | | | | % 12.78/2.47 | | | | | | REDUCE: (58), (60) imply: % 12.78/2.47 | | | | | | (61) apply(all_25_5, all_25_2, all_25_2) = all_59_0 % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | GROUND_INST: instantiating (22) with all_25_2, all_59_0, simplifying % 12.78/2.47 | | | | | | with (14), (61) gives: % 12.78/2.47 | | | | | | (62) all_59_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 12.78/2.47 | | | | | | member(all_25_2, all_25_4) = v0) % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | BETA: splitting (62) gives: % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | Case 1: % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | (63) all_59_0 = 0 % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | REDUCE: (55), (63) imply: % 12.78/2.47 | | | | | | | (64) $false % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | CLOSE: (64) is inconsistent. % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | Case 2: % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & member(all_25_2, all_25_4) = % 12.78/2.47 | | | | | | | v0) % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | DELTA: instantiating (65) with fresh symbol all_92_0 gives: % 12.78/2.47 | | | | | | | (66) ~ (all_92_0 = 0) & member(all_25_2, all_25_4) = all_92_0 % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | ALPHA: (66) implies: % 12.78/2.47 | | | | | | | (67) ~ (all_92_0 = 0) % 12.78/2.47 | | | | | | | (68) member(all_25_2, all_25_4) = all_92_0 % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | GROUND_INST: instantiating (7) with 0, all_92_0, all_25_4, % 12.78/2.47 | | | | | | | all_25_2, simplifying with (16), (68) gives: % 12.78/2.47 | | | | | | | (69) all_92_0 = 0 % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | REDUCE: (67), (69) imply: % 12.78/2.47 | | | | | | | (70) $false % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | | CLOSE: (70) is inconsistent. % 12.78/2.47 | | | | | | | % 12.78/2.47 | | | | | | End of split % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | Case 2: % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | (71) all_59_1 = all_25_3 % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | REDUCE: (58), (71) imply: % 12.78/2.47 | | | | | | (72) apply(all_25_5, all_25_3, all_25_2) = all_59_0 % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | GROUND_INST: instantiating (8) with 0, all_59_0, all_25_2, all_25_3, % 12.78/2.47 | | | | | | all_25_5, simplifying with (18), (72) gives: % 12.78/2.47 | | | | | | (73) all_59_0 = 0 % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | REDUCE: (55), (73) imply: % 12.78/2.47 | | | | | | (74) $false % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | | CLOSE: (74) is inconsistent. % 12.78/2.47 | | | | | | % 12.78/2.47 | | | | | End of split % 12.78/2.47 | | | | | % 12.78/2.47 | | | | End of split % 12.78/2.47 | | | | % 12.78/2.47 | | | Case 2: % 12.78/2.47 | | | | % 12.78/2.47 | | | | (75) ~ (all_43_1 = 0) % 12.78/2.47 | | | | % 12.78/2.47 | | | | REDUCE: (48), (75) imply: % 12.78/2.47 | | | | (76) $false % 12.78/2.47 | | | | % 12.78/2.47 | | | | CLOSE: (76) is inconsistent. % 12.78/2.47 | | | | % 12.78/2.47 | | | End of split % 12.78/2.47 | | | % 12.78/2.47 | | End of split % 12.78/2.47 | | % 12.78/2.47 | End of split % 12.78/2.47 | % 12.78/2.47 End of proof % 12.78/2.47 % SZS output end Proof for theBenchmark % 12.78/2.47 % 12.78/2.47 1869ms %------------------------------------------------------------------------------