%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 00:04:27 EDT 2023 % Result : Theorem 11.63s 2.32s % Output : Proof 16.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.37 % Computer : n020.cluster.edu % 0.16/0.37 % Model : x86_64 x86_64 % 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.37 % Memory : 8042.1875MB % 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.37 % CPULimit : 300 % 0.16/0.37 % WCLimit : 300 % 0.16/0.37 % DateTime : Sun Aug 27 03:42:44 EDT 2023 % 0.16/0.37 % CPUTime : % 0.23/0.65 ________ _____ % 0.23/0.65 ___ __ \_________(_)________________________________ % 0.23/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.23/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.23/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.23/0.65 % 0.23/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.23/0.65 (2023-06-19) % 0.23/0.65 % 0.23/0.65 (c) Philipp Rümmer, 2009-2023 % 0.23/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.23/0.65 Amanda Stjerna. % 0.23/0.65 Free software under BSD-3-Clause. % 0.23/0.65 % 0.23/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.23/0.65 % 0.23/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.23/0.66 Running up to 7 provers in parallel. % 0.23/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.23/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.23/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.23/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.23/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.23/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.23/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.22/1.16 Prover 4: Preprocessing ... % 3.22/1.17 Prover 1: Preprocessing ... % 3.22/1.21 Prover 2: Preprocessing ... % 3.22/1.21 Prover 5: Preprocessing ... % 3.22/1.21 Prover 0: Preprocessing ... % 3.22/1.21 Prover 6: Preprocessing ... % 3.22/1.21 Prover 3: Preprocessing ... % 7.71/1.77 Prover 1: Constructing countermodel ... % 7.71/1.77 Prover 6: Proving ... % 7.71/1.77 Prover 3: Constructing countermodel ... % 7.71/1.78 Prover 5: Proving ... % 7.71/1.82 Prover 2: Proving ... % 8.79/1.96 Prover 4: Constructing countermodel ... % 9.05/2.01 Prover 0: Proving ... % 11.17/2.32 Prover 2: proved (1643ms) % 11.63/2.32 % 11.63/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.63/2.32 % 11.63/2.32 Prover 0: proved (1652ms) % 11.63/2.32 % 11.63/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.63/2.32 % 11.63/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.63/2.32 Prover 5: stopped % 11.63/2.32 Prover 6: stopped % 11.63/2.33 Prover 3: stopped % 11.63/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.63/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.63/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.63/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.89/2.38 Prover 13: Preprocessing ... % 11.89/2.39 Prover 7: Preprocessing ... % 11.89/2.40 Prover 8: Preprocessing ... % 11.89/2.40 Prover 10: Preprocessing ... % 11.89/2.41 Prover 11: Preprocessing ... % 13.29/2.56 Prover 10: Warning: ignoring some quantifiers % 13.29/2.56 Prover 13: Warning: ignoring some quantifiers % 13.47/2.57 Prover 7: Warning: ignoring some quantifiers % 13.47/2.57 Prover 10: Constructing countermodel ... % 13.47/2.58 Prover 8: Warning: ignoring some quantifiers % 13.47/2.59 Prover 8: Constructing countermodel ... % 13.47/2.60 Prover 7: Constructing countermodel ... % 13.47/2.62 Prover 13: Constructing countermodel ... % 13.90/2.64 Prover 10: gave up % 13.90/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.90/2.68 Prover 7: gave up % 13.90/2.68 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.90/2.74 Prover 16: Preprocessing ... % 13.90/2.75 Prover 4: Found proof (size 126) % 13.90/2.75 Prover 4: proved (2072ms) % 13.90/2.75 Prover 13: stopped % 13.90/2.75 Prover 8: stopped % 13.90/2.75 Prover 1: stopped % 13.90/2.76 Prover 19: Preprocessing ... % 13.90/2.77 Prover 16: stopped % 13.90/2.78 Prover 11: Constructing countermodel ... % 14.76/2.79 Prover 11: stopped % 15.35/2.87 Prover 19: Warning: ignoring some quantifiers % 15.35/2.88 Prover 19: Constructing countermodel ... % 15.35/2.88 Prover 19: stopped % 15.35/2.88 % 15.35/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.35/2.88 % 15.56/2.91 % SZS output start Proof for theBenchmark % 15.56/2.91 Assumptions after simplification: % 15.56/2.91 --------------------------------- % 15.56/2.91 % 15.56/2.91 (on_path_properties) % 15.56/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.56/2.94 any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ % 15.56/2.94 (head_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 15.56/2.94 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v6 & % 15.56/2.94 in_path(v8, v2) = v9 & edge(v3) = v7 & tail_of(v3) = v8 & $i(v8) & ( ~ (v6 % 15.72/2.94 = 0) | (v9 = 0 & v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 15.72/2.94 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (in_path(v4, v2) = % 15.72/2.94 v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ~ $i(v3) | ~ % 15.72/2.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : % 15.72/2.94 ? [v9: any] : (on_path(v3, v2) = v6 & in_path(v8, v2) = v9 & head_of(v3) = % 15.72/2.94 v8 & edge(v3) = v7 & $i(v8) & ( ~ (v6 = 0) | (v9 = 0 & v7 = 0 & v5 = 0)))) % 15.72/2.94 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 15.72/2.94 (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.72/2.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] % 15.72/2.94 : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2) = v9 & in_path(v6, % 15.72/2.94 v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 & $i(v8) & $i(v6) & ( ~ % 15.72/2.94 (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 15.72/2.94 ! [v2: $i] : ! [v3: $i] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = % 15.72/2.94 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 15.72/2.94 $i] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & head_of(v3) = v4 & % 15.72/2.94 edge(v3) = 0 & tail_of(v3) = v5 & $i(v5) & $i(v4))) % 15.72/2.94 % 15.72/2.94 (path_properties) % 15.72/2.94 $i(empty) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = % 15.72/2.94 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 15.72/2.94 [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : (path_cons(v3, empty) % 15.72/2.94 = v5 & head_of(v3) = v4 & edge(v3) = 0 & tail_of(v3) = v0 & $i(v6) & % 15.72/2.94 $i(v5) & $i(v4) & $i(v3) & ( ~ (v5 = v2) | ~ (v4 = v1) | ( ! [v9: $i] : ( % 15.72/2.94 ~ (path_cons(v3, v9) = v2) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = % 15.72/2.94 0) & path(v1, v1, v9) = v10)) & ! [v9: $i] : ( ~ (path(v1, v1, % 15.72/2.94 v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v2) & % 15.72/2.94 path_cons(v3, v9) = v10 & $i(v10))))) & ((v8 = v2 & v7 = 0 & % 15.72/2.94 path_cons(v3, v6) = v2 & path(v4, v1, v6) = 0) | (v5 = v2 & v4 = % 15.72/2.94 v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, % 15.72/2.94 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 & % 15.72/2.94 vertex(v0) = 0)) % 15.72/2.94 % 15.72/2.94 (precedes_defn) % 15.72/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.72/2.95 MultipleValueBool] : ! [v6: $i] : ( ~ (precedes(v6, v4, v0) = 0) | ~ % 15.72/2.95 (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ % 15.72/2.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? % 15.72/2.95 [v8: any] : ? [v9: any] : (( ~ (v7 = 0) & sequential(v3, v6) = v7) | % 15.72/2.95 (precedes(v3, v4, v0) = v9 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & % 15.72/2.95 ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 15.72/2.95 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: MultipleValueBool] : ! [v6: % 15.72/2.95 $i] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~ % 15.72/2.95 (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.72/2.95 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: any] : ? [v9: any] : (( ~ (v7 = % 15.72/2.95 0) & precedes(v6, v4, v0) = v7) | (precedes(v3, v4, v0) = v9 & % 15.72/2.95 on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) % 15.72/2.95 | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.72/2.95 ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ % 15.72/2.95 (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.72/2.95 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sequential(v3, v4) = % 15.72/2.95 v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 15.72/2.95 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ % 15.72/2.95 $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) % 15.72/2.95 & ! [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: % 15.72/2.95 int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))))) & ! [v0: % 15.72/2.95 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.72/2.95 (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) % 15.72/2.95 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 15.72/2.95 any] : (precedes(v3, v4, v0) = v7 & on_path(v4, v0) = v6 & on_path(v3, v0) % 15.72/2.95 = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) % 15.72/2.95 % 15.72/2.95 (precedes_properties) % 15.72/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.72/2.95 any] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) % 15.72/2.95 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 15.72/2.95 any] : ? [v8: any] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : % 15.72/2.95 (precedes(v3, v4, v0) = v6 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & % 15.72/2.95 $i(v9) & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0 & ( ~ (v5 = 0) | ( ! [v12: $i] : % 15.72/2.95 ( ~ (precedes(v12, v4, v0) = 0) | ~ $i(v12) | ? [v13: int] : ( ~ % 15.72/2.95 (v13 = 0) & sequential(v3, v12) = v13)) & ! [v12: $i] : ( ~ % 15.72/2.95 (sequential(v3, v12) = 0) | ~ $i(v12) | ? [v13: int] : ( ~ % 15.72/2.95 (v13 = 0) & precedes(v12, v4, v0) = v13)))) & (v5 = 0 | (v11 = % 15.72/2.95 0 & v10 = 0 & precedes(v9, v4, v0) = 0 & sequential(v3, v9) = % 15.72/2.95 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.72/2.95 ! [v4: $i] : ( ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~ % 15.72/2.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 15.72/2.95 [v6: $i] : ? [v7: int] : ? [v8: int] : (sequential(v3, v4) = v5 & % 15.72/2.95 on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ( ~ (v5 = 0) | ( ! % 15.72/2.95 [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int] % 15.72/2.95 : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~ % 15.72/2.95 (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) % 15.72/2.95 & precedes(v9, v4, v0) = v10)))) & (v5 = 0 | (v8 = 0 & v7 = 0 & % 15.72/2.95 precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0)))) % 15.72/2.95 % 15.72/2.95 (shortest_path_defn) % 15.72/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | % 15.72/2.96 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.72/2.96 [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: % 15.72/2.96 int] : (length_of(v2) = v5 & path(v0, v1, v2) = v4 & $i(v6) & $i(v5) & ( ~ % 15.72/2.96 (v4 = 0) | (v7 = 0 & ~ (v9 = 0) & length_of(v6) = v8 & % 15.72/2.96 less_or_equal(v5, v8) = v9 & path(v0, v1, v6) = 0 & $i(v8))))) & ! % 15.72/2.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, v1, v2) = % 15.72/2.96 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : % 15.72/2.96 (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5 & $i(v5) & ( ~ (v4 = 0) % 15.72/2.96 | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : ! [v7: $i] : ( ~ % 15.72/2.96 (length_of(v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: any] : % 15.72/2.96 (less_or_equal(v5, v7) = v9 & path(v0, v1, v6) = v8 & ( ~ (v8 = 0) | % 15.72/2.96 v9 = 0))) & ! [v6: $i] : ( ~ (path(v0, v1, v6) = 0) | ~ $i(v6) % 15.72/2.96 | ? [v7: $i] : (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 & % 15.72/2.96 $i(v7))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.72/2.96 | ~ (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 15.72/2.96 $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: % 15.72/2.96 int] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v3 & $i(v5) & % 15.72/2.96 $i(v3) & (v4 = 0 | (v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 & % 15.72/2.96 less_or_equal(v3, v7) = v8 & path(v0, v1, v5) = 0 & $i(v7))))) & ! % 15.72/2.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) | % 15.72/2.96 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (length_of(v2) = v3 & % 15.72/2.96 path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 15.72/2.96 (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : % 15.72/2.96 (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = v6 & ( ~ (v6 = 0) | v7 % 15.72/2.96 = 0))) & ! [v4: $i] : ( ~ (path(v0, v1, v4) = 0) | ~ $i(v4) | ? % 15.72/2.96 [v5: $i] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0 & $i(v5))))) % 15.72/2.96 & ! [v0: $i] : ! [v1: $i] : ( ~ (shortest_path(v0, v0, v1) = 0) | ~ $i(v1) % 15.72/2.96 | ~ $i(v0)) % 15.72/2.96 % 15.72/2.96 (shortest_path_properties) % 15.72/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.72/2.96 $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (head_of(v3) = % 15.72/2.96 v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.72/2.96 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (precedes(v3, v2, v4) = % 15.72/2.96 v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) | ( ~ (v8 = 0) & ! [v9: $i] % 15.72/2.96 : ( ~ (head_of(v9) = v6) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) & % 15.72/2.96 tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = % 15.72/2.96 v5) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = % 15.72/2.96 v10 & $i(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.72/2.96 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | % 15.72/2.96 ~ (precedes(v3, v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.72/2.96 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 15.72/2.96 (precedes(v2, v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) & % 15.72/2.96 $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = % 15.72/2.96 v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) & tail_of(v9) = % 15.72/2.96 v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v7) | ~ $i(v9) % 15.72/2.96 | ? [v10: $i] : ( ~ (v10 = v8) & head_of(v9) = v10 & $i(v10))))))) % 15.72/2.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.72/2.96 (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ~ $i(v4) % 15.72/2.96 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] % 15.72/2.96 : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & head_of(v3) = v6 % 15.72/2.96 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ! [v8: $i] : ( ~ (head_of(v8) = % 15.72/2.96 v6) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v5) & tail_of(v8) = v9 & % 15.72/2.96 $i(v9))) & ! [v8: $i] : ( ~ (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: % 15.72/2.96 $i] : ( ~ (v9 = v6) & head_of(v8) = v9 & $i(v9))))) % 15.72/2.96 % 15.72/2.96 (vertices_and_edges) % 15.72/2.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.72/2.96 any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 15.72/2.96 (shortest_path(v0, v1, v4) = 0 & precedes(v2, v3, v4) = 0 & path(v0, v1, v4) = % 15.72/2.96 v9 & vertex(v1) = v6 & vertex(v0) = v5 & edge(v3) = v8 & edge(v2) = v7 & % 15.72/2.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ % 15.72/2.96 (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v3 = v2 | v1 = v0)) % 15.72/2.96 % 15.72/2.96 (function-axioms) % 15.72/2.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.72/2.97 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 15.72/2.97 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.72/2.97 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 15.72/2.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.72/2.97 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 15.72/2.97 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.72/2.97 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 15.72/2.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 15.72/2.97 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.72/2.97 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 15.72/2.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.72/2.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 15.72/2.97 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.97 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 15.72/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.72/2.97 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 15.72/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.72/2.97 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 15.72/2.97 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 15.72/2.97 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.72/2.97 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 15.72/2.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 15.72/2.97 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 15.72/2.97 $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 15.72/2.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.72/2.97 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 15.72/2.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 15.72/2.97 v0)) % 15.72/2.97 % 15.72/2.97 Further assumptions not needed in the proof: % 15.72/2.97 -------------------------------------------- % 15.72/2.97 complete_properties, edge_ends_are_vertices, graph_has_them_all, % 15.72/2.97 in_path_properties, length_defn, no_loops, path_defn, % 15.72/2.97 path_length_sequential_pairs, sequential_defn, sequential_pairs_and_triangles, % 15.72/2.97 triangle_defn % 15.72/2.97 % 15.72/2.97 Those formulas are unsatisfiable: % 15.72/2.97 --------------------------------- % 15.72/2.97 % 15.72/2.97 Begin of proof % 15.72/2.97 | % 15.72/2.97 | ALPHA: (path_properties) implies: % 15.72/2.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 15.72/2.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 & vertex(v0) = 0)) % 15.72/2.97 | % 15.72/2.97 | ALPHA: (on_path_properties) implies: % 15.72/2.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 15.72/2.97 | ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2) % 15.72/2.97 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 15.72/2.97 | ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2) % 15.72/2.97 | = v9 & in_path(v6, v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 & % 15.72/2.97 | $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0)))) % 15.72/2.97 | % 15.72/2.97 | ALPHA: (precedes_defn) implies: % 15.72/2.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.72/2.97 | ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, % 15.72/2.97 | v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.72/2.97 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sequential(v3, % 15.72/2.97 | v4) = v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = v6 & ( ~ (v7 % 15.72/2.98 | = 0) | ~ (v6 = 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ % 15.72/2.98 | (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ % 15.72/2.98 | (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~ % 15.72/2.98 | (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ % 15.72/2.98 | (v10 = 0) & precedes(v9, v4, v0) = v10)))))) % 15.72/2.98 | % 15.72/2.98 | ALPHA: (precedes_properties) implies: % 15.72/2.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.72/2.98 | ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) % 15.72/2.98 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 15.72/2.98 | [v6: $i] : ? [v7: int] : ? [v8: int] : (sequential(v3, v4) = v5 & % 15.72/2.98 | on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ( ~ (v5 = 0) | % 15.72/2.98 | ( ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? % 15.72/2.98 | [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! % 15.72/2.98 | [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: % 15.72/2.98 | int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))) & (v5 % 15.72/2.98 | = 0 | (v8 = 0 & v7 = 0 & precedes(v6, v4, v0) = 0 & % 15.72/2.98 | sequential(v3, v6) = 0)))) % 15.72/2.98 | % 15.72/2.98 | ALPHA: (shortest_path_defn) implies: % 15.72/2.98 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, % 15.72/2.98 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 15.72/2.98 | (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : % 15.72/2.98 | ! [v5: $i] : ( ~ (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] : % 15.72/2.98 | ? [v7: any] : (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = v6 % 15.72/2.98 | & ( ~ (v6 = 0) | v7 = 0))) & ! [v4: $i] : ( ~ (path(v0, v1, % 15.72/2.98 | v4) = 0) | ~ $i(v4) | ? [v5: $i] : (length_of(v4) = v5 & % 15.72/2.98 | less_or_equal(v3, v5) = 0 & $i(v5))))) % 15.72/2.98 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, % 15.72/2.98 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 15.72/2.98 | : ? [v5: $i] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5 % 15.72/2.98 | & $i(v5) & ( ~ (v4 = 0) | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : ! % 15.72/2.98 | [v7: $i] : ( ~ (length_of(v6) = v7) | ~ $i(v6) | ? [v8: any] % 15.72/2.98 | : ? [v9: any] : (less_or_equal(v5, v7) = v9 & path(v0, v1, % 15.72/2.98 | v6) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v6: $i] : ( ~ % 15.72/2.98 | (path(v0, v1, v6) = 0) | ~ $i(v6) | ? [v7: $i] : % 15.72/2.98 | (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 & % 15.72/2.98 | $i(v7))))))) % 15.72/2.98 | % 15.72/2.98 | ALPHA: (shortest_path_properties) implies: % 15.72/2.98 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.72/2.98 | ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | % 15.72/2.98 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 15.72/2.98 | $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, % 15.72/2.98 | v4) = v7 & head_of(v3) = v6 & tail_of(v2) = v5 & $i(v6) & $i(v5) % 15.72/2.98 | & ! [v8: $i] : ( ~ (head_of(v8) = v6) | ~ $i(v8) | ? [v9: $i] : % 15.72/2.98 | ( ~ (v9 = v5) & tail_of(v8) = v9 & $i(v9))) & ! [v8: $i] : ( ~ % 15.72/2.98 | (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v6) & % 15.72/2.98 | head_of(v8) = v9 & $i(v9))))) % 15.72/2.98 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.72/2.98 | ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3, % 15.72/2.98 | v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 15.72/2.98 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (precedes(v2, % 15.72/2.99 | v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) & % 15.72/2.99 | $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ % 15.72/2.99 | (head_of(v9) = v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 15.72/2.99 | v7) & tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ % 15.72/2.99 | (tail_of(v9) = v7) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 15.72/2.99 | v8) & head_of(v9) = v10 & $i(v10))))))) % 15.72/2.99 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.72/2.99 | ! [v5: $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ % 15.72/2.99 | (head_of(v3) = v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 15.72/2.99 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 15.72/2.99 | (precedes(v3, v2, v4) = v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) % 15.72/2.99 | | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = v6) | ~ $i(v9) % 15.72/2.99 | | ? [v10: $i] : ( ~ (v10 = v5) & tail_of(v9) = v10 & % 15.72/2.99 | $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v5) | ~ % 15.72/2.99 | $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = v10 & % 15.72/2.99 | $i(v10))))))) % 15.72/2.99 | % 15.72/2.99 | ALPHA: (function-axioms) implies: % 15.72/2.99 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.72/2.99 | : (v1 = v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) % 15.72/2.99 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.72/2.99 | : ! [v3: $i] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, % 15.72/2.99 | v2) = v0)) % 15.72/2.99 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (path(v4, v3, v2) = v1) | % 15.72/2.99 | ~ (path(v4, v3, v2) = v0)) % 15.72/2.99 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = % 15.72/2.99 | v1) | ~ (precedes(v4, v3, v2) = v0)) % 15.72/2.99 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.72/2.99 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (shortest_path(v4, v3, v2) % 15.72/2.99 | = v1) | ~ (shortest_path(v4, v3, v2) = v0)) % 15.72/2.99 | % 15.72/2.99 | DELTA: instantiating (vertices_and_edges) with fresh symbols all_20_0, % 15.72/2.99 | all_20_1, all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, % 15.72/2.99 | all_20_8, all_20_9 gives: % 15.72/2.99 | (15) shortest_path(all_20_9, all_20_8, all_20_5) = 0 & precedes(all_20_7, % 15.72/2.99 | all_20_6, all_20_5) = 0 & path(all_20_9, all_20_8, all_20_5) = % 15.72/2.99 | all_20_0 & vertex(all_20_8) = all_20_3 & vertex(all_20_9) = all_20_4 & % 15.72/2.99 | edge(all_20_6) = all_20_1 & edge(all_20_7) = all_20_2 & $i(all_20_5) & % 15.72/2.99 | $i(all_20_6) & $i(all_20_7) & $i(all_20_8) & $i(all_20_9) & ( ~ % 15.72/2.99 | (all_20_0 = 0) | ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~ % 15.72/2.99 | (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 % 15.72/2.99 | = all_20_9) % 15.72/2.99 | % 15.72/2.99 | ALPHA: (15) implies: % 15.72/2.99 | (16) $i(all_20_9) % 15.72/2.99 | (17) $i(all_20_8) % 15.72/2.99 | (18) $i(all_20_7) % 15.72/2.99 | (19) $i(all_20_6) % 15.72/2.99 | (20) $i(all_20_5) % 15.72/2.99 | (21) edge(all_20_7) = all_20_2 % 15.72/2.99 | (22) edge(all_20_6) = all_20_1 % 15.72/2.99 | (23) vertex(all_20_9) = all_20_4 % 15.72/2.99 | (24) vertex(all_20_8) = all_20_3 % 15.72/2.99 | (25) path(all_20_9, all_20_8, all_20_5) = all_20_0 % 15.72/2.99 | (26) precedes(all_20_7, all_20_6, all_20_5) = 0 % 15.72/2.99 | (27) shortest_path(all_20_9, all_20_8, all_20_5) = 0 % 15.72/2.99 | (28) ~ (all_20_0 = 0) | ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~ % 15.72/2.99 | (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 = % 15.72/2.99 | all_20_9 % 15.72/2.99 | % 15.72/2.99 | GROUND_INST: instantiating (6) with all_20_9, all_20_8, all_20_5, all_20_0, % 15.72/2.99 | simplifying with (16), (17), (20), (25) gives: % 15.72/3.00 | (29) ? [v0: any] : ? [v1: $i] : (shortest_path(all_20_9, all_20_8, % 15.72/3.00 | all_20_5) = v0 & length_of(all_20_5) = v1 & $i(v1) & ( ~ (v0 = 0) % 15.72/3.00 | | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v2: $i] : ! [v3: % 15.72/3.00 | $i] : ( ~ (length_of(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 15.72/3.00 | [v5: any] : (less_or_equal(v1, v3) = v5 & path(all_20_9, % 15.72/3.00 | all_20_8, v2) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2: % 15.72/3.00 | $i] : ( ~ (path(all_20_9, all_20_8, v2) = 0) | ~ $i(v2) | ? % 15.72/3.00 | [v3: $i] : (length_of(v2) = v3 & less_or_equal(v1, v3) = 0 & % 15.72/3.00 | $i(v3)))))) % 15.72/3.00 | % 15.72/3.00 | GROUND_INST: instantiating (7) with all_20_9, all_20_8, all_20_7, all_20_6, % 15.72/3.00 | all_20_5, simplifying with (16), (17), (18), (19), (20), (26), % 15.72/3.00 | (27) gives: % 15.72/3.00 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 15.72/3.00 | precedes(all_20_6, all_20_7, all_20_5) = v2 & head_of(all_20_6) = v1 % 15.72/3.00 | & tail_of(all_20_7) = v0 & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ % 15.72/3.00 | (head_of(v3) = v1) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v0) & % 15.72/3.00 | tail_of(v3) = v4 & $i(v4))) & ! [v3: $i] : ( ~ (tail_of(v3) = % 15.72/3.00 | v0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & head_of(v3) = v4 % 15.72/3.00 | & $i(v4)))) % 15.72/3.00 | % 15.72/3.00 | GROUND_INST: instantiating (8) with all_20_9, all_20_8, all_20_6, all_20_7, % 15.72/3.00 | all_20_5, 0, simplifying with (16), (17), (18), (19), (20), (26), % 15.72/3.00 | (27) gives: % 15.72/3.00 | (31) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = 0) & % 15.72/3.00 | precedes(all_20_6, all_20_7, all_20_5) = v0 & head_of(all_20_7) = v2 % 15.72/3.00 | & tail_of(all_20_6) = v1 & $i(v2) & $i(v1)) % 15.72/3.00 | % 15.72/3.00 | GROUND_INST: instantiating (5) with all_20_9, all_20_8, all_20_5, simplifying % 15.72/3.00 | with (16), (17), (20), (27) gives: % 15.72/3.00 | (32) ? [v0: $i] : (length_of(all_20_5) = v0 & path(all_20_9, all_20_8, % 15.72/3.00 | all_20_5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 15.72/3.00 | (length_of(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 15.72/3.00 | (less_or_equal(v0, v2) = v4 & path(all_20_9, all_20_8, v1) = v3 & % 15.72/3.00 | ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (path(all_20_9, % 15.72/3.00 | all_20_8, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (length_of(v1) % 15.72/3.00 | = v2 & less_or_equal(v0, v2) = 0 & $i(v2)))) % 15.72/3.00 | % 15.72/3.00 | DELTA: instantiating (31) with fresh symbols all_27_0, all_27_1, all_27_2 % 15.72/3.00 | gives: % 15.72/3.00 | (33) ~ (all_27_2 = 0) & precedes(all_20_6, all_20_7, all_20_5) = all_27_2 % 15.72/3.00 | & head_of(all_20_7) = all_27_0 & tail_of(all_20_6) = all_27_1 & % 15.72/3.00 | $i(all_27_0) & $i(all_27_1) % 15.72/3.00 | % 15.72/3.00 | ALPHA: (33) implies: % 15.72/3.00 | (34) tail_of(all_20_6) = all_27_1 % 15.72/3.00 | (35) head_of(all_20_7) = all_27_0 % 15.72/3.00 | (36) precedes(all_20_6, all_20_7, all_20_5) = all_27_2 % 15.72/3.00 | % 15.72/3.00 | DELTA: instantiating (32) with fresh symbol all_29_0 gives: % 15.72/3.00 | (37) length_of(all_20_5) = all_29_0 & path(all_20_9, all_20_8, all_20_5) = % 15.72/3.00 | 0 & $i(all_29_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (length_of(v0) = % 15.72/3.00 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 15.72/3.00 | (less_or_equal(all_29_0, v1) = v3 & path(all_20_9, all_20_8, v0) = % 15.72/3.00 | v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (path(all_20_9, % 15.72/3.00 | all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (length_of(v0) = % 15.72/3.00 | v1 & less_or_equal(all_29_0, v1) = 0 & $i(v1))) % 15.72/3.00 | % 15.72/3.00 | ALPHA: (37) implies: % 15.72/3.00 | (38) path(all_20_9, all_20_8, all_20_5) = 0 % 15.72/3.00 | % 15.72/3.00 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1, all_32_2 % 15.72/3.00 | gives: % 15.72/3.00 | (39) ~ (all_32_0 = 0) & precedes(all_20_6, all_20_7, all_20_5) = all_32_0 % 15.72/3.00 | & head_of(all_20_6) = all_32_1 & tail_of(all_20_7) = all_32_2 & % 15.72/3.00 | $i(all_32_1) & $i(all_32_2) & ! [v0: $i] : ( ~ (head_of(v0) = % 15.72/3.00 | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) & % 15.72/3.00 | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 15.72/3.00 | all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1) & % 15.72/3.00 | head_of(v0) = v1 & $i(v1))) % 15.72/3.00 | % 15.72/3.00 | ALPHA: (39) implies: % 15.72/3.00 | (40) ~ (all_32_0 = 0) % 15.72/3.00 | (41) tail_of(all_20_7) = all_32_2 % 15.72/3.00 | (42) head_of(all_20_6) = all_32_1 % 15.72/3.00 | (43) precedes(all_20_6, all_20_7, all_20_5) = all_32_0 % 15.72/3.00 | % 15.72/3.00 | DELTA: instantiating (29) with fresh symbols all_35_0, all_35_1 gives: % 15.72/3.00 | (44) shortest_path(all_20_9, all_20_8, all_20_5) = all_35_1 & % 15.72/3.00 | length_of(all_20_5) = all_35_0 & $i(all_35_0) & ( ~ (all_35_1 = 0) | % 15.72/3.00 | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0: $i] : ! [v1: $i] % 15.72/3.00 | : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 15.72/3.00 | any] : (less_or_equal(all_35_0, v1) = v3 & path(all_20_9, % 15.72/3.00 | all_20_8, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 15.72/3.00 | : ( ~ (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i] % 15.72/3.00 | : (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 & % 15.72/3.01 | $i(v1))))) % 15.72/3.01 | % 15.72/3.01 | ALPHA: (44) implies: % 15.72/3.01 | (45) shortest_path(all_20_9, all_20_8, all_20_5) = all_35_1 % 15.72/3.01 | (46) ~ (all_35_1 = 0) | (all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0: % 15.72/3.01 | $i] : ! [v1: $i] : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: % 15.72/3.01 | any] : ? [v3: any] : (less_or_equal(all_35_0, v1) = v3 & % 15.72/3.01 | path(all_20_9, all_20_8, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & % 15.72/3.01 | ! [v0: $i] : ( ~ (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ? % 15.72/3.01 | [v1: $i] : (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 & % 15.72/3.01 | $i(v1)))) % 15.72/3.01 | % 15.72/3.01 | GROUND_INST: instantiating (12) with all_20_0, 0, all_20_5, all_20_8, % 15.72/3.01 | all_20_9, simplifying with (25), (38) gives: % 15.72/3.01 | (47) all_20_0 = 0 % 15.72/3.01 | % 15.72/3.01 | GROUND_INST: instantiating (13) with all_27_2, all_32_0, all_20_5, all_20_7, % 15.72/3.01 | all_20_6, simplifying with (36), (43) gives: % 15.72/3.01 | (48) all_32_0 = all_27_2 % 15.72/3.01 | % 15.72/3.01 | GROUND_INST: instantiating (14) with 0, all_35_1, all_20_5, all_20_8, % 15.72/3.01 | all_20_9, simplifying with (27), (45) gives: % 15.72/3.01 | (49) all_35_1 = 0 % 15.72/3.01 | % 15.72/3.01 | REDUCE: (40), (48) imply: % 15.72/3.01 | (50) ~ (all_27_2 = 0) % 15.72/3.01 | % 15.72/3.01 | BETA: splitting (46) gives: % 15.72/3.01 | % 15.72/3.01 | Case 1: % 15.72/3.01 | | % 15.72/3.01 | | (51) ~ (all_35_1 = 0) % 15.72/3.01 | | % 15.72/3.01 | | REDUCE: (49), (51) imply: % 15.72/3.01 | | (52) $false % 15.72/3.01 | | % 15.72/3.01 | | CLOSE: (52) is inconsistent. % 15.72/3.01 | | % 15.72/3.01 | Case 2: % 15.72/3.01 | | % 15.72/3.01 | | (53) all_20_0 = 0 & ~ (all_20_8 = all_20_9) & ! [v0: $i] : ! [v1: $i] % 15.72/3.01 | | : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 15.72/3.01 | | : (less_or_equal(all_35_0, v1) = v3 & path(all_20_9, all_20_8, v0) % 15.72/3.01 | | = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 15.72/3.01 | | (path(all_20_9, all_20_8, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.72/3.01 | | (length_of(v0) = v1 & less_or_equal(all_35_0, v1) = 0 & $i(v1))) % 15.72/3.01 | | % 15.72/3.01 | | ALPHA: (53) implies: % 15.72/3.01 | | (54) ~ (all_20_8 = all_20_9) % 15.72/3.01 | | % 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_7, all_20_7, % 15.72/3.01 | | all_20_5, all_32_2, all_27_0, simplifying with (16), (17), % 15.72/3.01 | | (18), (20), (27), (35), (41) gives: % 15.72/3.01 | | (55) ? [v0: any] : ? [v1: any] : (precedes(all_20_7, all_20_7, % 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_7, all_20_7, all_20_5) = v0 & ( % 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) = % 15.72/3.01 | | all_27_0) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_32_2) % 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~ % 15.72/3.01 | | (tail_of(v2) = all_32_2) | ~ $i(v2) | ? [v3: any] : ( ~ % 15.72/3.01 | | (v3 = all_27_0) & head_of(v2) = v3 & $i(v3)))))) % 15.72/3.01 | | % 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_6, all_20_6, % 15.72/3.01 | | all_20_5, all_27_1, all_32_1, simplifying with (16), (17), % 15.72/3.01 | | (19), (20), (27), (34), (42) gives: % 15.72/3.01 | | (56) ? [v0: any] : ? [v1: any] : (precedes(all_20_6, all_20_6, % 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_6, all_20_6, all_20_5) = v0 & ( % 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) = % 15.72/3.01 | | all_32_1) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_27_1) % 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~ % 15.72/3.01 | | (tail_of(v2) = all_27_1) | ~ $i(v2) | ? [v3: any] : ( ~ % 15.72/3.01 | | (v3 = all_32_1) & head_of(v2) = v3 & $i(v3)))))) % 15.72/3.01 | | % 15.72/3.01 | | GROUND_INST: instantiating (9) with all_20_9, all_20_8, all_20_7, all_20_6, % 15.72/3.01 | | all_20_5, all_32_2, all_32_1, simplifying with (16), (17), % 15.72/3.01 | | (18), (19), (20), (27), (41), (42) gives: % 15.72/3.01 | | (57) ? [v0: any] : ? [v1: any] : (precedes(all_20_6, all_20_7, % 15.72/3.01 | | all_20_5) = v1 & precedes(all_20_7, all_20_6, all_20_5) = v0 & ( % 15.72/3.01 | | ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) = % 15.72/3.01 | | all_32_1) | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_32_2) % 15.72/3.01 | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~ % 15.72/3.01 | | (tail_of(v2) = all_32_2) | ~ $i(v2) | ? [v3: any] : ( ~ % 15.72/3.01 | | (v3 = all_32_1) & head_of(v2) = v3 & $i(v3)))))) % 15.72/3.01 | | % 15.72/3.02 | | GROUND_INST: instantiating (4) with all_20_5, all_20_9, all_20_8, all_20_7, % 15.72/3.02 | | all_20_6, simplifying with (16), (17), (18), (19), (20), (26), % 15.72/3.02 | | (38) gives: % 15.72/3.02 | | (58) ? [v0: any] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 15.72/3.02 | | (sequential(all_20_7, all_20_6) = v0 & on_path(all_20_6, all_20_5) = % 15.72/3.02 | | 0 & on_path(all_20_7, all_20_5) = 0 & $i(v1) & ( ~ (v0 = 0) | ( ! % 15.72/3.02 | | [v4: $i] : ( ~ (precedes(v4, all_20_6, all_20_5) = 0) | ~ % 15.72/3.02 | | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & sequential(all_20_7, % 15.72/3.02 | | v4) = v5)) & ! [v4: $i] : ( ~ (sequential(all_20_7, v4) % 15.72/3.02 | | = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 15.72/3.02 | | precedes(v4, all_20_6, all_20_5) = v5)))) & (v0 = 0 | (v3 % 15.72/3.02 | | = 0 & v2 = 0 & precedes(v1, all_20_6, all_20_5) = 0 & % 15.72/3.02 | | sequential(all_20_7, v1) = 0))) % 15.72/3.02 | | % 15.72/3.02 | | GROUND_INST: instantiating (2) with all_20_9, all_20_8, all_20_5, all_20_6, % 15.72/3.02 | | all_20_1, simplifying with (16), (17), (19), (20), (22), (38) % 15.72/3.02 | | gives: % 15.72/3.02 | | (59) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 15.72/3.02 | | any] : (on_path(all_20_6, all_20_5) = v0 & in_path(v3, all_20_5) = % 15.72/3.02 | | v4 & in_path(v1, all_20_5) = v2 & head_of(all_20_6) = v1 & % 15.72/3.02 | | tail_of(all_20_6) = v3 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 % 15.72/3.02 | | & v2 = 0 & all_20_1 = 0))) % 15.72/3.02 | | % 15.72/3.02 | | GROUND_INST: instantiating (2) with all_20_9, all_20_8, all_20_5, all_20_7, % 15.72/3.02 | | all_20_2, simplifying with (16), (17), (18), (20), (21), (38) % 15.72/3.02 | | gives: % 15.72/3.02 | | (60) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 15.72/3.02 | | any] : (on_path(all_20_7, all_20_5) = v0 & in_path(v3, all_20_5) = % 15.72/3.02 | | v4 & in_path(v1, all_20_5) = v2 & head_of(all_20_7) = v1 & % 15.72/3.02 | | tail_of(all_20_7) = v3 & $i(v3) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 % 15.72/3.02 | | & v2 = 0 & all_20_2 = 0))) % 15.72/3.02 | | % 15.72/3.02 | | GROUND_INST: instantiating (1) with all_20_9, all_20_8, all_20_5, % 15.72/3.02 | | simplifying with (16), (17), (20), (38) gives: % 15.72/3.02 | | (61) vertex(all_20_8) = 0 & vertex(all_20_9) = 0 % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (61) implies: % 15.72/3.02 | | (62) vertex(all_20_9) = 0 % 15.72/3.02 | | (63) vertex(all_20_8) = 0 % 15.72/3.02 | | % 15.72/3.02 | | GROUND_INST: instantiating (3) with all_20_5, all_20_9, all_20_8, all_20_6, % 15.72/3.02 | | all_20_7, all_27_2, simplifying with (16), (17), (18), (19), % 15.72/3.02 | | (20), (36), (38) gives: % 15.72/3.02 | | (64) all_27_2 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 15.72/3.02 | | (sequential(all_20_6, all_20_7) = v2 & on_path(all_20_6, all_20_5) = % 15.72/3.02 | | v0 & on_path(all_20_7, all_20_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) % 15.72/3.02 | | | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (precedes(v3, all_20_7, % 15.72/3.02 | | all_20_5) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) % 15.72/3.02 | | & sequential(all_20_6, v3) = v4)) & ! [v3: $i] : ( ~ % 15.72/3.02 | | (sequential(all_20_6, v3) = 0) | ~ $i(v3) | ? [v4: int] : % 15.72/3.02 | | ( ~ (v4 = 0) & precedes(v3, all_20_7, all_20_5) = v4))))) % 15.72/3.02 | | % 15.72/3.02 | | GROUND_INST: instantiating (8) with all_20_9, all_20_8, all_20_7, all_20_6, % 15.72/3.02 | | all_20_5, all_27_2, simplifying with (16), (17), (18), (19), % 15.72/3.02 | | (20), (27), (36) gives: % 15.72/3.02 | | (65) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (precedes(all_20_7, % 15.72/3.02 | | all_20_6, all_20_5) = v0 & head_of(all_20_6) = v2 & % 15.72/3.02 | | tail_of(all_20_7) = v1 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ~ % 15.72/3.02 | | (all_27_2 = 0) & ! [v3: $i] : ( ~ (head_of(v3) = v2) | ~ % 15.72/3.02 | | $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & tail_of(v3) = v4 & % 15.72/3.02 | | $i(v4))) & ! [v3: $i] : ( ~ (tail_of(v3) = v1) | ~ % 15.72/3.02 | | $i(v3) | ? [v4: $i] : ( ~ (v4 = v2) & head_of(v3) = v4 & % 15.72/3.02 | | $i(v4)))))) % 15.72/3.02 | | % 15.72/3.02 | | DELTA: instantiating (60) with fresh symbols all_86_0, all_86_1, all_86_2, % 15.72/3.02 | | all_86_3, all_86_4 gives: % 15.72/3.02 | | (66) on_path(all_20_7, all_20_5) = all_86_4 & in_path(all_86_1, all_20_5) % 15.72/3.02 | | = all_86_0 & in_path(all_86_3, all_20_5) = all_86_2 & % 15.72/3.02 | | head_of(all_20_7) = all_86_3 & tail_of(all_20_7) = all_86_1 & % 15.72/3.02 | | $i(all_86_1) & $i(all_86_3) & ( ~ (all_86_4 = 0) | (all_86_0 = 0 & % 15.72/3.02 | | all_86_2 = 0 & all_20_2 = 0)) % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (66) implies: % 15.72/3.02 | | (67) on_path(all_20_7, all_20_5) = all_86_4 % 15.72/3.02 | | (68) ~ (all_86_4 = 0) | (all_86_0 = 0 & all_86_2 = 0 & all_20_2 = 0) % 15.72/3.02 | | % 15.72/3.02 | | DELTA: instantiating (59) with fresh symbols all_90_0, all_90_1, all_90_2, % 15.72/3.02 | | all_90_3, all_90_4 gives: % 15.72/3.02 | | (69) on_path(all_20_6, all_20_5) = all_90_4 & in_path(all_90_1, all_20_5) % 15.72/3.02 | | = all_90_0 & in_path(all_90_3, all_20_5) = all_90_2 & % 15.72/3.02 | | head_of(all_20_6) = all_90_3 & tail_of(all_20_6) = all_90_1 & % 15.72/3.02 | | $i(all_90_1) & $i(all_90_3) & ( ~ (all_90_4 = 0) | (all_90_0 = 0 & % 15.72/3.02 | | all_90_2 = 0 & all_20_1 = 0)) % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (69) implies: % 15.72/3.02 | | (70) on_path(all_20_6, all_20_5) = all_90_4 % 15.72/3.02 | | (71) ~ (all_90_4 = 0) | (all_90_0 = 0 & all_90_2 = 0 & all_20_1 = 0) % 15.72/3.02 | | % 15.72/3.02 | | DELTA: instantiating (55) with fresh symbols all_94_0, all_94_1 gives: % 15.72/3.02 | | (72) precedes(all_20_7, all_20_7, all_20_5) = all_94_0 & % 15.72/3.02 | | precedes(all_20_7, all_20_7, all_20_5) = all_94_1 & ( ~ (all_94_1 = % 15.72/3.02 | | 0) | ( ~ (all_94_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) = % 15.72/3.02 | | all_27_0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) & % 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) % 15.72/3.02 | | = all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_27_0) % 15.72/3.02 | | & head_of(v0) = v1 & $i(v1))))) % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (72) implies: % 15.72/3.02 | | (73) precedes(all_20_7, all_20_7, all_20_5) = all_94_1 % 15.72/3.02 | | (74) precedes(all_20_7, all_20_7, all_20_5) = all_94_0 % 15.72/3.02 | | % 15.72/3.02 | | DELTA: instantiating (57) with fresh symbols all_96_0, all_96_1 gives: % 15.72/3.02 | | (75) precedes(all_20_6, all_20_7, all_20_5) = all_96_0 & % 15.72/3.02 | | precedes(all_20_7, all_20_6, all_20_5) = all_96_1 & ( ~ (all_96_1 = % 15.72/3.02 | | 0) | ( ~ (all_96_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) = % 15.72/3.02 | | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_2) & % 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) % 15.72/3.02 | | = all_32_2) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1) % 15.72/3.02 | | & head_of(v0) = v1 & $i(v1))))) % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (75) implies: % 15.72/3.02 | | (76) precedes(all_20_7, all_20_6, all_20_5) = all_96_1 % 15.72/3.02 | | (77) precedes(all_20_6, all_20_7, all_20_5) = all_96_0 % 15.72/3.02 | | % 15.72/3.02 | | DELTA: instantiating (56) with fresh symbols all_98_0, all_98_1 gives: % 15.72/3.02 | | (78) precedes(all_20_6, all_20_6, all_20_5) = all_98_0 & % 15.72/3.02 | | precedes(all_20_6, all_20_6, all_20_5) = all_98_1 & ( ~ (all_98_1 = % 15.72/3.02 | | 0) | ( ~ (all_98_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) = % 15.72/3.02 | | all_32_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_27_1) & % 15.72/3.02 | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) % 15.72/3.02 | | = all_27_1) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_32_1) % 15.72/3.02 | | & head_of(v0) = v1 & $i(v1))))) % 15.72/3.02 | | % 15.72/3.02 | | ALPHA: (78) implies: % 15.72/3.02 | | (79) precedes(all_20_6, all_20_6, all_20_5) = all_98_1 % 15.72/3.03 | | (80) precedes(all_20_6, all_20_6, all_20_5) = all_98_0 % 15.72/3.03 | | % 15.72/3.03 | | DELTA: instantiating (65) with fresh symbols all_100_0, all_100_1, all_100_2 % 15.72/3.03 | | gives: % 15.72/3.03 | | (81) precedes(all_20_7, all_20_6, all_20_5) = all_100_2 & % 15.72/3.03 | | head_of(all_20_6) = all_100_0 & tail_of(all_20_7) = all_100_1 & % 15.72/3.03 | | $i(all_100_0) & $i(all_100_1) & ( ~ (all_100_2 = 0) | ( ~ (all_27_2 % 15.72/3.03 | | = 0) & ! [v0: $i] : ( ~ (head_of(v0) = all_100_0) | ~ $i(v0) % 15.72/3.03 | | | ? [v1: any] : ( ~ (v1 = all_100_1) & tail_of(v0) = v1 & % 15.72/3.03 | | $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = all_100_1) | ~ % 15.72/3.03 | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_100_0) & head_of(v0) = % 15.72/3.03 | | v1 & $i(v1))))) % 15.72/3.03 | | % 15.72/3.03 | | ALPHA: (81) implies: % 15.72/3.03 | | (82) precedes(all_20_7, all_20_6, all_20_5) = all_100_2 % 15.72/3.03 | | % 15.72/3.03 | | DELTA: instantiating (58) with fresh symbols all_102_0, all_102_1, % 15.72/3.03 | | all_102_2, all_102_3 gives: % 15.72/3.03 | | (83) sequential(all_20_7, all_20_6) = all_102_3 & on_path(all_20_6, % 15.72/3.03 | | all_20_5) = 0 & on_path(all_20_7, all_20_5) = 0 & $i(all_102_2) & % 15.72/3.03 | | ( ~ (all_102_3 = 0) | ( ! [v0: $i] : ( ~ (precedes(v0, all_20_6, % 15.72/3.03 | | all_20_5) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 15.72/3.03 | | sequential(all_20_7, v0) = v1)) & ! [v0: $i] : ( ~ % 15.72/3.03 | | (sequential(all_20_7, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 15.72/3.03 | | ~ (v1 = 0) & precedes(v0, all_20_6, all_20_5) = v1)))) & % 15.72/3.03 | | (all_102_3 = 0 | (all_102_0 = 0 & all_102_1 = 0 & % 15.72/3.03 | | precedes(all_102_2, all_20_6, all_20_5) = 0 & % 15.72/3.03 | | sequential(all_20_7, all_102_2) = 0)) % 15.72/3.03 | | % 15.72/3.03 | | ALPHA: (83) implies: % 15.72/3.03 | | (84) on_path(all_20_7, all_20_5) = 0 % 15.72/3.03 | | (85) on_path(all_20_6, all_20_5) = 0 % 15.72/3.03 | | % 15.72/3.03 | | BETA: splitting (64) gives: % 15.72/3.03 | | % 15.72/3.03 | | Case 1: % 15.72/3.03 | | | % 15.72/3.03 | | | (86) all_27_2 = 0 % 15.72/3.03 | | | % 15.72/3.03 | | | REDUCE: (50), (86) imply: % 15.72/3.03 | | | (87) $false % 15.72/3.03 | | | % 15.72/3.03 | | | CLOSE: (87) is inconsistent. % 15.72/3.03 | | | % 15.72/3.03 | | Case 2: % 15.72/3.03 | | | % 15.72/3.03 | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sequential(all_20_6, % 15.72/3.03 | | | all_20_7) = v2 & on_path(all_20_6, all_20_5) = v0 & % 15.72/3.03 | | | on_path(all_20_7, all_20_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 15.72/3.03 | | | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (precedes(v3, all_20_7, % 15.72/3.03 | | | all_20_5) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 15.72/3.03 | | | 0) & sequential(all_20_6, v3) = v4)) & ! [v3: $i] : ( % 15.72/3.03 | | | ~ (sequential(all_20_6, v3) = 0) | ~ $i(v3) | ? [v4: % 15.72/3.03 | | | int] : ( ~ (v4 = 0) & precedes(v3, all_20_7, all_20_5) = % 15.72/3.03 | | | v4))))) % 15.72/3.03 | | | % 15.72/3.03 | | | DELTA: instantiating (88) with fresh symbols all_115_0, all_115_1, % 15.72/3.03 | | | all_115_2 gives: % 15.72/3.03 | | | (89) sequential(all_20_6, all_20_7) = all_115_0 & on_path(all_20_6, % 15.72/3.03 | | | all_20_5) = all_115_2 & on_path(all_20_7, all_20_5) = all_115_1 % 15.72/3.03 | | | & ( ~ (all_115_1 = 0) | ~ (all_115_2 = 0) | ( ~ (all_115_0 = 0) & % 15.72/3.03 | | | ! [v0: $i] : ( ~ (precedes(v0, all_20_7, all_20_5) = 0) | ~ % 15.72/3.03 | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & sequential(all_20_6, % 15.72/3.03 | | | v0) = v1)) & ! [v0: $i] : ( ~ (sequential(all_20_6, v0) % 15.72/3.03 | | | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 15.72/3.03 | | | precedes(v0, all_20_7, all_20_5) = v1)))) % 15.72/3.03 | | | % 15.72/3.03 | | | ALPHA: (89) implies: % 15.72/3.03 | | | (90) on_path(all_20_7, all_20_5) = all_115_1 % 15.72/3.03 | | | (91) on_path(all_20_6, all_20_5) = all_115_2 % 15.72/3.03 | | | % 15.72/3.03 | | | GROUND_INST: instantiating (10) with all_20_4, 0, all_20_9, simplifying % 15.72/3.03 | | | with (23), (62) gives: % 15.72/3.03 | | | (92) all_20_4 = 0 % 15.72/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (10) with all_20_3, 0, all_20_8, simplifying % 16.18/3.03 | | | with (24), (63) gives: % 16.18/3.03 | | | (93) all_20_3 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (11) with all_86_4, all_115_1, all_20_5, % 16.18/3.03 | | | all_20_7, simplifying with (67), (90) gives: % 16.18/3.03 | | | (94) all_115_1 = all_86_4 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (11) with 0, all_115_1, all_20_5, all_20_7, % 16.18/3.03 | | | simplifying with (84), (90) gives: % 16.18/3.03 | | | (95) all_115_1 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (11) with all_90_4, all_115_2, all_20_5, % 16.18/3.03 | | | all_20_6, simplifying with (70), (91) gives: % 16.18/3.03 | | | (96) all_115_2 = all_90_4 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (11) with 0, all_115_2, all_20_5, all_20_6, % 16.18/3.03 | | | simplifying with (85), (91) gives: % 16.18/3.03 | | | (97) all_115_2 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_94_1, all_94_0, all_20_5, % 16.18/3.03 | | | all_20_7, all_20_7, simplifying with (73), (74) gives: % 16.18/3.03 | | | (98) all_94_0 = all_94_1 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (13) with 0, all_100_2, all_20_5, all_20_6, % 16.18/3.03 | | | all_20_7, simplifying with (26), (82) gives: % 16.18/3.03 | | | (99) all_100_2 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_96_1, all_100_2, all_20_5, % 16.18/3.03 | | | all_20_6, all_20_7, simplifying with (76), (82) gives: % 16.18/3.03 | | | (100) all_100_2 = all_96_1 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_27_2, all_96_0, all_20_5, % 16.18/3.03 | | | all_20_7, all_20_6, simplifying with (36), (77) gives: % 16.18/3.03 | | | (101) all_96_0 = all_27_2 % 16.18/3.03 | | | % 16.18/3.03 | | | GROUND_INST: instantiating (13) with all_98_1, all_98_0, all_20_5, % 16.18/3.03 | | | all_20_6, all_20_6, simplifying with (79), (80) gives: % 16.18/3.03 | | | (102) all_98_0 = all_98_1 % 16.18/3.03 | | | % 16.18/3.03 | | | COMBINE_EQS: (94), (95) imply: % 16.18/3.03 | | | (103) all_86_4 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | SIMP: (103) implies: % 16.18/3.03 | | | (104) all_86_4 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | COMBINE_EQS: (96), (97) imply: % 16.18/3.03 | | | (105) all_90_4 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | COMBINE_EQS: (99), (100) imply: % 16.18/3.03 | | | (106) all_96_1 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | SIMP: (106) implies: % 16.18/3.03 | | | (107) all_96_1 = 0 % 16.18/3.03 | | | % 16.18/3.03 | | | BETA: splitting (68) gives: % 16.18/3.03 | | | % 16.18/3.03 | | | Case 1: % 16.18/3.03 | | | | % 16.18/3.03 | | | | (108) ~ (all_86_4 = 0) % 16.18/3.03 | | | | % 16.18/3.03 | | | | REDUCE: (104), (108) imply: % 16.18/3.03 | | | | (109) $false % 16.18/3.03 | | | | % 16.18/3.03 | | | | CLOSE: (109) is inconsistent. % 16.18/3.03 | | | | % 16.18/3.03 | | | Case 2: % 16.18/3.03 | | | | % 16.18/3.03 | | | | (110) all_86_0 = 0 & all_86_2 = 0 & all_20_2 = 0 % 16.18/3.03 | | | | % 16.18/3.03 | | | | ALPHA: (110) implies: % 16.18/3.03 | | | | (111) all_20_2 = 0 % 16.18/3.03 | | | | % 16.18/3.03 | | | | BETA: splitting (71) gives: % 16.18/3.03 | | | | % 16.18/3.03 | | | | Case 1: % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | (112) ~ (all_90_4 = 0) % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | REDUCE: (105), (112) imply: % 16.18/3.03 | | | | | (113) $false % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | CLOSE: (113) is inconsistent. % 16.18/3.03 | | | | | % 16.18/3.03 | | | | Case 2: % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | (114) all_90_0 = 0 & all_90_2 = 0 & all_20_1 = 0 % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | ALPHA: (114) implies: % 16.18/3.03 | | | | | (115) all_20_1 = 0 % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | BETA: splitting (28) gives: % 16.18/3.03 | | | | | % 16.18/3.03 | | | | | Case 1: % 16.18/3.03 | | | | | | % 16.18/3.03 | | | | | | (116) ~ (all_20_0 = 0) % 16.18/3.03 | | | | | | % 16.18/3.03 | | | | | | REDUCE: (47), (116) imply: % 16.18/3.03 | | | | | | (117) $false % 16.18/3.03 | | | | | | % 16.18/3.04 | | | | | | CLOSE: (117) is inconsistent. % 16.18/3.04 | | | | | | % 16.18/3.04 | | | | | Case 2: % 16.18/3.04 | | | | | | % 16.18/3.04 | | | | | | (118) ~ (all_20_1 = 0) | ~ (all_20_2 = 0) | ~ (all_20_3 = 0) | % 16.18/3.04 | | | | | | ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 = % 16.18/3.04 | | | | | | all_20_9 % 16.18/3.04 | | | | | | % 16.18/3.04 | | | | | | BETA: splitting (118) gives: % 16.18/3.04 | | | | | | % 16.18/3.04 | | | | | | Case 1: % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | (119) ~ (all_20_1 = 0) % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | REDUCE: (115), (119) imply: % 16.18/3.04 | | | | | | | (120) $false % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | CLOSE: (120) is inconsistent. % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | Case 2: % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | (121) ~ (all_20_2 = 0) | ~ (all_20_3 = 0) | ~ (all_20_4 = 0) % 16.18/3.04 | | | | | | | | all_20_6 = all_20_7 | all_20_8 = all_20_9 % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | BETA: splitting (121) gives: % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | | Case 1: % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | (122) ~ (all_20_2 = 0) % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | REDUCE: (111), (122) imply: % 16.18/3.04 | | | | | | | | (123) $false % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | CLOSE: (123) is inconsistent. % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | Case 2: % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | (124) ~ (all_20_3 = 0) | ~ (all_20_4 = 0) | all_20_6 = % 16.18/3.04 | | | | | | | | all_20_7 | all_20_8 = all_20_9 % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | BETA: splitting (124) gives: % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | | Case 1: % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | (125) ~ (all_20_3 = 0) % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | REDUCE: (93), (125) imply: % 16.18/3.04 | | | | | | | | | (126) $false % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | CLOSE: (126) is inconsistent. % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | Case 2: % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | (127) ~ (all_20_4 = 0) | all_20_6 = all_20_7 | all_20_8 = % 16.18/3.04 | | | | | | | | | all_20_9 % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | BETA: splitting (127) gives: % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | | Case 1: % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | (128) ~ (all_20_4 = 0) % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | REDUCE: (92), (128) imply: % 16.18/3.04 | | | | | | | | | | (129) $false % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | CLOSE: (129) is inconsistent. % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | Case 2: % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | (130) all_20_6 = all_20_7 | all_20_8 = all_20_9 % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | BETA: splitting (130) gives: % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | Case 1: % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | (131) all_20_6 = all_20_7 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | REDUCE: (79), (131) imply: % 16.18/3.04 | | | | | | | | | | | (132) precedes(all_20_7, all_20_7, all_20_5) = all_98_1 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | REDUCE: (36), (131) imply: % 16.18/3.04 | | | | | | | | | | | (133) precedes(all_20_7, all_20_7, all_20_5) = all_27_2 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | REDUCE: (26), (131) imply: % 16.18/3.04 | | | | | | | | | | | (134) precedes(all_20_7, all_20_7, all_20_5) = 0 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_94_1, 0, all_20_5, % 16.18/3.04 | | | | | | | | | | | all_20_7, all_20_7, simplifying with (73), (134) % 16.18/3.04 | | | | | | | | | | | gives: % 16.18/3.04 | | | | | | | | | | | (135) all_94_1 = 0 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_94_1, all_98_1, % 16.18/3.04 | | | | | | | | | | | all_20_5, all_20_7, all_20_7, simplifying with % 16.18/3.04 | | | | | | | | | | | (73), (132) gives: % 16.18/3.04 | | | | | | | | | | | (136) all_98_1 = all_94_1 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_27_2, all_98_1, % 16.18/3.04 | | | | | | | | | | | all_20_5, all_20_7, all_20_7, simplifying with % 16.18/3.04 | | | | | | | | | | | (132), (133) gives: % 16.18/3.04 | | | | | | | | | | | (137) all_98_1 = all_27_2 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | COMBINE_EQS: (136), (137) imply: % 16.18/3.04 | | | | | | | | | | | (138) all_94_1 = all_27_2 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | SIMP: (138) implies: % 16.18/3.04 | | | | | | | | | | | (139) all_94_1 = all_27_2 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | COMBINE_EQS: (135), (139) imply: % 16.18/3.04 | | | | | | | | | | | (140) all_27_2 = 0 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | REDUCE: (50), (140) imply: % 16.18/3.04 | | | | | | | | | | | (141) $false % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | CLOSE: (141) is inconsistent. % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | Case 2: % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | (142) all_20_8 = all_20_9 % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | REDUCE: (54), (142) imply: % 16.18/3.04 | | | | | | | | | | | (143) $false % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | | CLOSE: (143) is inconsistent. % 16.18/3.04 | | | | | | | | | | | % 16.18/3.04 | | | | | | | | | | End of split % 16.18/3.04 | | | | | | | | | | % 16.18/3.04 | | | | | | | | | End of split % 16.18/3.04 | | | | | | | | | % 16.18/3.04 | | | | | | | | End of split % 16.18/3.04 | | | | | | | | % 16.18/3.04 | | | | | | | End of split % 16.18/3.04 | | | | | | | % 16.18/3.04 | | | | | | End of split % 16.18/3.04 | | | | | | % 16.18/3.04 | | | | | End of split % 16.18/3.04 | | | | | % 16.18/3.04 | | | | End of split % 16.18/3.04 | | | | % 16.18/3.04 | | | End of split % 16.18/3.04 | | | % 16.18/3.04 | | End of split % 16.18/3.04 | | % 16.18/3.04 | End of split % 16.18/3.04 | % 16.18/3.04 End of proof % 16.18/3.04 % SZS output end Proof for theBenchmark % 16.18/3.04 % 16.18/3.04 2392ms %------------------------------------------------------------------------------