%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 68.95s 9.84s % Output : Proof 70.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Aug 27 03:45:23 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.99/1.15 Prover 4: Preprocessing ... % 2.99/1.15 Prover 1: Preprocessing ... % 3.65/1.19 Prover 5: Preprocessing ... % 3.65/1.19 Prover 0: Preprocessing ... % 3.65/1.19 Prover 6: Preprocessing ... % 3.65/1.19 Prover 2: Preprocessing ... % 3.65/1.19 Prover 3: Preprocessing ... % 7.43/1.77 Prover 6: Proving ... % 7.43/1.77 Prover 3: Constructing countermodel ... % 7.43/1.77 Prover 2: Proving ... % 7.43/1.77 Prover 5: Proving ... % 7.43/1.79 Prover 1: Constructing countermodel ... % 7.63/1.88 Prover 0: Proving ... % 7.63/1.89 Prover 4: Constructing countermodel ... % 68.95/9.77 Prover 4: Found proof (size 351) % 68.95/9.77 Prover 4: proved (9115ms) % 68.95/9.77 Prover 3: stopped % 68.95/9.77 Prover 2: stopped % 68.95/9.77 Prover 0: stopped % 68.95/9.78 Prover 6: stopped % 68.95/9.78 Prover 1: stopped % 68.95/9.83 Prover 5: stopped % 68.95/9.84 % 68.95/9.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 68.95/9.84 % 69.32/9.88 % SZS output start Proof for theBenchmark % 69.32/9.88 Assumptions after simplification: % 69.32/9.88 --------------------------------- % 69.32/9.88 % 69.32/9.88 (complete_properties) % 69.52/9.92 ~ complete | ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vertex(v1) = 0) | ~ % 69.52/9.92 (vertex(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? % 69.52/9.92 [v4: $i] : (head_of(v2) = v3 & edge(v2) = 0 & tail_of(v2) = v4 & $i(v4) & % 69.52/9.92 $i(v3) & $i(v2) & ((v4 = v1 & v3 = v0) | (v4 = v0 & v3 = v1)))) % 69.52/9.92 % 69.52/9.92 (edge_ends_are_vertices) % 69.52/9.92 ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? [v2: any] % 69.52/9.92 : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (vertex(v4) = v5 & vertex(v1) % 69.52/9.92 = v3 & edge(v0) = v2 & tail_of(v0) = v4 & $i(v4) & ( ~ (v2 = 0) | (v5 = 0 % 69.52/9.92 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ % 69.52/9.92 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 69.52/9.92 (vertex(v3) = v4 & vertex(v1) = v5 & head_of(v0) = v3 & edge(v0) = v2 & % 69.52/9.92 $i(v3) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ( ~ (edge(v0) % 69.52/9.92 = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (vertex(v2) = 0 & % 69.52/9.92 vertex(v1) = 0 & head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) & $i(v1))) % 69.52/9.92 % 69.52/9.92 (graph_has_them_all) % 69.52/9.93 $i(graph) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (number_of_in(v0, % 69.52/9.93 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(v0, % 69.52/9.93 graph) = v3 & less_or_equal(v2, v3) = 0 & $i(v3))) % 69.52/9.93 % 69.52/9.93 (maximal_path_length) % 69.52/9.93 $i(graph) & $i(triangles) & $i(n1) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 69.52/9.93 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 69.52/9.93 minus(v4, n1) = v5 & number_of_in(triangles, graph) = v0 & shortest_path(v2, % 69.52/9.93 v3, v1) = 0 & length_of(v1) = v4 & less_or_equal(v5, v0) = v6 & $i(v5) & % 69.52/9.93 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & complete) % 69.52/9.93 % 69.52/9.93 (no_loops) % 69.52/9.93 ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? [v2: any] % 69.52/9.93 : ? [v3: $i] : (edge(v0) = v2 & tail_of(v0) = v3 & $i(v3) & ( ~ (v3 = v1) | % 69.52/9.93 ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ % 69.52/9.93 $i(v0) | ? [v2: any] : ? [v3: $i] : (head_of(v0) = v3 & edge(v0) = v2 & % 69.52/9.93 $i(v3) & ( ~ (v3 = v1) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (edge(v0) = 0) % 69.52/9.93 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & head_of(v0) = v1 & % 69.52/9.93 tail_of(v0) = v2 & $i(v2) & $i(v1))) % 69.52/9.93 % 69.52/9.93 (on_path_properties) % 69.79/9.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 69.79/9.94 any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | ~ % 69.79/9.94 (head_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 69.79/9.94 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v6 & % 69.79/9.94 in_path(v8, v2) = v9 & edge(v3) = v7 & tail_of(v3) = v8 & $i(v8) & ( ~ (v6 % 69.79/9.94 = 0) | (v9 = 0 & v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 69.79/9.94 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (in_path(v4, v2) = % 69.79/9.94 v5) | ~ (path(v0, v1, v2) = 0) | ~ (tail_of(v3) = v4) | ~ $i(v3) | ~ % 69.79/9.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : % 69.79/9.94 ? [v9: any] : (on_path(v3, v2) = v6 & in_path(v8, v2) = v9 & head_of(v3) = % 69.79/9.94 v8 & edge(v3) = v7 & $i(v8) & ( ~ (v6 = 0) | (v9 = 0 & v7 = 0 & v5 = 0)))) % 69.79/9.94 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 69.79/9.94 (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 69.79/9.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] % 69.79/9.94 : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2) = v9 & in_path(v6, % 69.79/9.94 v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 & $i(v8) & $i(v6) & ( ~ % 69.79/9.94 (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 69.79/9.94 ! [v2: $i] : ! [v3: $i] : ( ~ (on_path(v3, v2) = 0) | ~ (path(v0, v1, v2) = % 69.79/9.94 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 69.79/9.94 $i] : (in_path(v5, v2) = 0 & in_path(v4, v2) = 0 & head_of(v3) = v4 & % 69.79/9.94 edge(v3) = 0 & tail_of(v3) = v5 & $i(v5) & $i(v4))) % 69.79/9.94 % 69.79/9.94 (path_length_sequential_pairs) % 69.79/9.95 $i(n1) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 69.79/9.95 (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 69.79/9.95 ? [v4: $i] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 69.79/9.95 length_of(v2) = v4 & $i(v4) & $i(v3))) % 69.79/9.95 % 69.79/9.95 (path_properties) % 69.79/9.95 $i(empty) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = % 69.79/9.95 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 69.79/9.95 [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : (path_cons(v3, empty) % 69.79/9.95 = v5 & head_of(v3) = v4 & edge(v3) = 0 & tail_of(v3) = v0 & $i(v6) & % 69.79/9.95 $i(v5) & $i(v4) & $i(v3) & ( ~ (v5 = v2) | ~ (v4 = v1) | ( ! [v9: $i] : ( % 69.79/9.95 ~ (path_cons(v3, v9) = v2) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = % 69.79/9.95 0) & path(v1, v1, v9) = v10)) & ! [v9: $i] : ( ~ (path(v1, v1, % 69.79/9.95 v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v2) & % 69.79/9.95 path_cons(v3, v9) = v10 & $i(v10))))) & ((v8 = v2 & v7 = 0 & % 69.79/9.95 path_cons(v3, v6) = v2 & path(v4, v1, v6) = 0) | (v5 = v2 & v4 = % 69.79/9.95 v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, % 69.79/9.95 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 & % 69.79/9.95 vertex(v0) = 0)) % 69.79/9.95 % 69.79/9.95 (precedes_defn) % 69.84/9.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 69.84/9.96 MultipleValueBool] : ! [v6: $i] : ( ~ (precedes(v6, v4, v0) = 0) | ~ % 69.84/9.96 (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ % 69.84/9.96 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? % 69.84/9.96 [v8: any] : ? [v9: any] : (( ~ (v7 = 0) & sequential(v3, v6) = v7) | % 69.84/9.96 (precedes(v3, v4, v0) = v9 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & % 69.84/9.96 ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 69.84/9.96 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: MultipleValueBool] : ! [v6: % 69.84/9.96 $i] : ( ~ (sequential(v3, v6) = 0) | ~ (sequential(v3, v4) = v5) | ~ % 69.84/9.96 (path(v1, v2, v0) = 0) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 69.84/9.96 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: any] : ? [v9: any] : (( ~ (v7 = % 69.84/9.96 0) & precedes(v6, v4, v0) = v7) | (precedes(v3, v4, v0) = v9 & % 69.84/9.96 on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) % 69.84/9.96 | v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 69.84/9.96 ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ % 69.84/9.96 (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 69.84/9.96 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sequential(v3, v4) = % 69.84/9.96 v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 69.84/9.96 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ % 69.84/9.96 $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) % 69.84/9.96 & ! [v9: $i] : ( ~ (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: % 69.84/9.96 int] : ( ~ (v10 = 0) & precedes(v9, v4, v0) = v10)))))) & ! [v0: % 69.84/9.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 69.84/9.96 (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) % 69.84/9.96 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 69.84/9.96 any] : (precedes(v3, v4, v0) = v7 & on_path(v4, v0) = v6 & on_path(v3, v0) % 69.84/9.96 = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) % 69.84/9.96 % 69.84/9.96 (precedes_properties) % 69.84/9.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 69.84/9.97 any] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) % 69.84/9.97 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 69.84/9.97 any] : ? [v8: any] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : % 69.84/9.97 (precedes(v3, v4, v0) = v6 & on_path(v4, v0) = v8 & on_path(v3, v0) = v7 & % 69.84/9.97 $i(v9) & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0 & ( ~ (v5 = 0) | ( ! [v12: $i] : % 69.84/9.97 ( ~ (precedes(v12, v4, v0) = 0) | ~ $i(v12) | ? [v13: int] : ( ~ % 69.84/9.97 (v13 = 0) & sequential(v3, v12) = v13)) & ! [v12: $i] : ( ~ % 69.84/9.97 (sequential(v3, v12) = 0) | ~ $i(v12) | ? [v13: int] : ( ~ % 69.84/9.97 (v13 = 0) & precedes(v12, v4, v0) = v13)))) & (v5 = 0 | (v11 = % 69.84/9.97 0 & v10 = 0 & precedes(v9, v4, v0) = 0 & sequential(v3, v9) = % 69.84/9.97 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 69.84/9.97 ! [v4: $i] : ( ~ (precedes(v3, v4, v0) = 0) | ~ (path(v1, v2, v0) = 0) | ~ % 69.84/9.97 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 69.84/9.97 [v6: $i] : ? [v7: int] : ? [v8: int] : (sequential(v3, v4) = v5 & % 69.84/9.97 on_path(v4, v0) = 0 & on_path(v3, v0) = 0 & $i(v6) & ( ~ (v5 = 0) | ( ! % 69.84/9.97 [v9: $i] : ( ~ (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int] % 69.84/9.97 : ( ~ (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~ % 69.84/9.97 (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) % 69.84/9.97 & precedes(v9, v4, v0) = v10)))) & (v5 = 0 | (v8 = 0 & v7 = 0 & % 69.84/9.97 precedes(v6, v4, v0) = 0 & sequential(v3, v6) = 0)))) % 69.84/9.97 % 69.84/9.97 (sequential_is_triangle) % 69.84/9.97 ~ complete | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 69.84/9.97 $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) % 69.84/9.97 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] % 69.84/9.97 : ? [v6: $i] : ? [v7: int] : ($i(v6) & ((v7 = 0 & triangle(v2, v3, v6) = % 69.84/9.97 0) | ( ~ (v5 = 0) & sequential(v2, v3) = v5)))) & ! [v0: $i] : ! % 69.84/9.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (shortest_path(v0, % 69.84/9.97 v1, v4) = 0) | ~ (sequential(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | % 69.84/9.97 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: % 69.84/9.97 int] : ($i(v6) & ((v7 = 0 & triangle(v2, v3, v6) = 0) | ( ~ (v5 = 0) & % 69.84/9.97 precedes(v2, v3, v4) = v5))))) % 69.84/9.97 % 69.84/9.97 (sequential_pairs_and_triangles) % 69.84/9.97 $i(triangles) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 69.84/9.97 : ( ~ (path(v1, v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 69.84/9.97 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ? % 69.84/9.97 [v9: int] : ($i(v6) & $i(v5) & ((v9 = 0 & v8 = 0 & v7 = 0 & sequential(v5, % 69.84/9.97 v6) = 0 & on_path(v6, v0) = 0 & on_path(v5, v0) = 0 & ! [v10: $i] : % 69.84/9.97 ( ~ (triangle(v5, v6, v10) = 0) | ~ $i(v10))) | (v4 = v3 & % 69.84/9.97 number_of_in(triangles, v0) = v3 & number_of_in(sequential_pairs, v0) % 69.84/9.97 = v3 & $i(v3))))) % 69.84/9.97 % 69.84/9.97 (shortest_path_defn) % 69.84/9.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | % 69.84/9.98 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 69.84/9.98 [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: % 69.84/9.98 int] : (length_of(v2) = v5 & path(v0, v1, v2) = v4 & $i(v6) & $i(v5) & ( ~ % 69.84/9.98 (v4 = 0) | (v7 = 0 & ~ (v9 = 0) & length_of(v6) = v8 & % 69.84/9.98 less_or_equal(v5, v8) = v9 & path(v0, v1, v6) = 0 & $i(v8))))) & ! % 69.84/9.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, v1, v2) = % 69.84/9.98 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : % 69.84/9.98 (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5 & $i(v5) & ( ~ (v4 = 0) % 69.84/9.98 | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : ! [v7: $i] : ( ~ % 69.84/9.98 (length_of(v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: any] : % 69.84/9.98 (less_or_equal(v5, v7) = v9 & path(v0, v1, v6) = v8 & ( ~ (v8 = 0) | % 69.84/9.98 v9 = 0))) & ! [v6: $i] : ( ~ (path(v0, v1, v6) = 0) | ~ $i(v6) % 69.84/9.98 | ? [v7: $i] : (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 & % 69.84/9.98 $i(v7))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 69.84/9.98 | ~ (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 69.84/9.98 $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: % 69.84/9.98 int] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v3 & $i(v5) & % 69.84/9.98 $i(v3) & (v4 = 0 | (v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 & % 69.84/9.98 less_or_equal(v3, v7) = v8 & path(v0, v1, v5) = 0 & $i(v7))))) & ! % 69.84/9.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) | % 69.84/9.98 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (length_of(v2) = v3 & % 69.84/9.98 path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 69.84/9.98 (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : % 69.84/9.98 (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = v6 & ( ~ (v6 = 0) | v7 % 69.84/9.98 = 0))) & ! [v4: $i] : ( ~ (path(v0, v1, v4) = 0) | ~ $i(v4) | ? % 69.84/9.98 [v5: $i] : (length_of(v4) = v5 & less_or_equal(v3, v5) = 0 & $i(v5))))) % 69.84/9.98 & ! [v0: $i] : ! [v1: $i] : ( ~ (shortest_path(v0, v0, v1) = 0) | ~ $i(v1) % 69.84/9.98 | ~ $i(v0)) % 69.84/9.98 % 69.84/9.98 (shortest_path_properties) % 69.84/9.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 69.84/9.99 $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (head_of(v3) = % 69.84/9.99 v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 69.84/9.99 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (precedes(v3, v2, v4) = % 69.84/9.99 v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = 0) | ( ~ (v8 = 0) & ! [v9: $i] % 69.84/9.99 : ( ~ (head_of(v9) = v6) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) & % 69.84/9.99 tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = % 69.84/9.99 v5) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = % 69.84/9.99 v10 & $i(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 69.84/9.99 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | % 69.84/9.99 ~ (precedes(v3, v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 69.84/9.99 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 69.84/9.99 (precedes(v2, v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) & % 69.84/9.99 $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = % 69.84/9.99 v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = v7) & tail_of(v9) = % 69.84/9.99 v10 & $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v7) | ~ $i(v9) % 69.84/9.99 | ? [v10: $i] : ( ~ (v10 = v8) & head_of(v9) = v10 & $i(v10))))))) % 69.84/9.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 69.84/9.99 (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, v4) = 0) | ~ $i(v4) % 69.84/9.99 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] % 69.84/9.99 : ? [v7: int] : ( ~ (v7 = 0) & precedes(v3, v2, v4) = v7 & head_of(v3) = v6 % 69.84/9.99 & tail_of(v2) = v5 & $i(v6) & $i(v5) & ! [v8: $i] : ( ~ (head_of(v8) = % 69.84/9.99 v6) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v5) & tail_of(v8) = v9 & % 69.84/9.99 $i(v9))) & ! [v8: $i] : ( ~ (tail_of(v8) = v5) | ~ $i(v8) | ? [v9: % 69.84/9.99 $i] : ( ~ (v9 = v6) & head_of(v8) = v9 & $i(v9))))) % 69.84/9.99 % 69.84/9.99 (function-axioms) % 69.84/9.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 69.84/9.99 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 69.84/9.99 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.84/9.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 69.84/9.99 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 69.84/9.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 69.84/9.99 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 69.84/9.99 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.84/9.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 69.84/9.99 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 69.84/9.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 69.84/9.99 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 69.84/9.99 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 69.84/9.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 69.84/9.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 69.84/9.99 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.84/9.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 69.84/9.99 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 69.84/9.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.84/9.99 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 69.84/9.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.84/9.99 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 69.84/9.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 69.84/9.99 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 69.84/9.99 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 69.84/9.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 69.84/9.99 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 69.84/9.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 69.84/9.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 69.84/9.99 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 69.84/9.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 69.84/9.99 v0)) % 69.84/9.99 % 69.84/9.99 Further assumptions not needed in the proof: % 69.84/9.99 -------------------------------------------- % 69.84/9.99 in_path_properties, length_defn, path_defn, sequential_defn, triangle_defn % 69.84/9.99 % 69.84/9.99 Those formulas are unsatisfiable: % 69.84/9.99 --------------------------------- % 69.84/9.99 % 69.84/9.99 Begin of proof % 69.84/9.99 | % 69.84/9.99 | ALPHA: (no_loops) implies: % 69.84/10.00 | (1) ! [v0: $i] : ( ~ (edge(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 69.84/10.00 | $i] : ( ~ (v2 = v1) & head_of(v0) = v1 & tail_of(v0) = v2 & $i(v2) % 69.84/10.00 | & $i(v1))) % 69.84/10.00 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ $i(v0) | ? % 69.84/10.00 | [v2: any] : ? [v3: $i] : (head_of(v0) = v3 & edge(v0) = v2 & $i(v3) % 69.84/10.00 | & ( ~ (v3 = v1) | ~ (v2 = 0)))) % 69.84/10.00 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? % 69.84/10.00 | [v2: any] : ? [v3: $i] : (edge(v0) = v2 & tail_of(v0) = v3 & $i(v3) % 69.84/10.00 | & ( ~ (v3 = v1) | ~ (v2 = 0)))) % 69.84/10.00 | % 69.84/10.00 | ALPHA: (edge_ends_are_vertices) implies: % 69.84/10.00 | (4) ! [v0: $i] : ( ~ (edge(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 69.84/10.00 | $i] : (vertex(v2) = 0 & vertex(v1) = 0 & head_of(v0) = v1 & % 69.84/10.00 | tail_of(v0) = v2 & $i(v2) & $i(v1))) % 69.84/10.00 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (tail_of(v0) = v1) | ~ $i(v0) | ? % 69.84/10.00 | [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : (vertex(v3) = % 69.84/10.00 | v4 & vertex(v1) = v5 & head_of(v0) = v3 & edge(v0) = v2 & $i(v3) & % 69.84/10.00 | ( ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) % 69.84/10.00 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (head_of(v0) = v1) | ~ $i(v0) | ? % 69.84/10.00 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (vertex(v4) = % 69.84/10.00 | v5 & vertex(v1) = v3 & edge(v0) = v2 & tail_of(v0) = v4 & $i(v4) & % 69.84/10.00 | ( ~ (v2 = 0) | (v5 = 0 & v3 = 0)))) % 69.84/10.00 | % 69.84/10.00 | ALPHA: (path_properties) implies: % 69.84/10.00 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 69.84/10.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (vertex(v1) = 0 & vertex(v0) = 0)) % 69.84/10.01 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 69.84/10.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 69.84/10.01 | [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : (path_cons(v3, % 69.84/10.01 | empty) = v5 & head_of(v3) = v4 & edge(v3) = 0 & tail_of(v3) = v0 % 69.84/10.01 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v5 = v2) | ~ (v4 = v1) % 69.84/10.01 | | ( ! [v9: $i] : ( ~ (path_cons(v3, v9) = v2) | ~ $i(v9) | ? % 69.84/10.01 | [v10: int] : ( ~ (v10 = 0) & path(v1, v1, v9) = v10)) & ! % 69.84/10.01 | [v9: $i] : ( ~ (path(v1, v1, v9) = 0) | ~ $i(v9) | ? [v10: % 69.84/10.01 | $i] : ( ~ (v10 = v2) & path_cons(v3, v9) = v10 & % 69.84/10.01 | $i(v10))))) & ((v8 = v2 & v7 = 0 & path_cons(v3, v6) = v2 & % 69.84/10.01 | path(v4, v1, v6) = 0) | (v5 = v2 & v4 = v1)))) % 69.84/10.01 | % 69.84/10.01 | ALPHA: (on_path_properties) implies: % 70.11/10.01 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 70.11/10.01 | ( ~ (path(v0, v1, v2) = 0) | ~ (edge(v3) = v4) | ~ $i(v3) | ~ $i(v2) % 70.11/10.01 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 70.11/10.01 | ? [v8: $i] : ? [v9: any] : (on_path(v3, v2) = v5 & in_path(v8, v2) % 70.11/10.01 | = v9 & in_path(v6, v2) = v7 & head_of(v3) = v6 & tail_of(v3) = v8 & % 70.11/10.01 | $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & v4 = 0)))) % 70.11/10.01 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.01 | ! [v5: any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | % 70.11/10.01 | ~ (tail_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.11/10.01 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 70.11/10.01 | (on_path(v3, v2) = v6 & in_path(v8, v2) = v9 & head_of(v3) = v8 & % 70.11/10.01 | edge(v3) = v7 & $i(v8) & ( ~ (v6 = 0) | (v9 = 0 & v7 = 0 & v5 = % 70.11/10.01 | 0)))) % 70.11/10.01 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.01 | ! [v5: any] : ( ~ (in_path(v4, v2) = v5) | ~ (path(v0, v1, v2) = 0) | % 70.11/10.01 | ~ (head_of(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.11/10.01 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 70.11/10.01 | (on_path(v3, v2) = v6 & in_path(v8, v2) = v9 & edge(v3) = v7 & % 70.11/10.01 | tail_of(v3) = v8 & $i(v8) & ( ~ (v6 = 0) | (v9 = 0 & v7 = 0 & v5 = % 70.11/10.01 | 0)))) % 70.11/10.01 | % 70.11/10.01 | ALPHA: (precedes_defn) implies: % 70.11/10.01 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.01 | ( ~ (sequential(v3, v4) = 0) | ~ (path(v1, v2, v0) = 0) | ~ $i(v4) | % 70.11/10.01 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 70.11/10.01 | [v6: any] : ? [v7: any] : (precedes(v3, v4, v0) = v7 & on_path(v4, % 70.11/10.01 | v0) = v6 & on_path(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 70.11/10.01 | v7 = 0))) % 70.11/10.01 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.01 | ! [v5: int] : (v5 = 0 | ~ (precedes(v3, v4, v0) = v5) | ~ (path(v1, % 70.11/10.02 | v2, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 70.11/10.02 | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 70.11/10.02 | (sequential(v3, v4) = v8 & on_path(v4, v0) = v7 & on_path(v3, v0) = % 70.11/10.02 | v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ % 70.11/10.02 | (precedes(v9, v4, v0) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ % 70.11/10.02 | (v10 = 0) & sequential(v3, v9) = v10)) & ! [v9: $i] : ( ~ % 70.11/10.02 | (sequential(v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ % 70.11/10.02 | (v10 = 0) & precedes(v9, v4, v0) = v10)))))) % 70.11/10.02 | % 70.11/10.02 | ALPHA: (precedes_properties) implies: % 70.11/10.02 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.02 | ! [v5: any] : ( ~ (sequential(v3, v4) = v5) | ~ (path(v1, v2, v0) = % 70.11/10.02 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 70.11/10.02 | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: % 70.11/10.02 | int] : ? [v11: int] : (precedes(v3, v4, v0) = v6 & on_path(v4, % 70.11/10.02 | v0) = v8 & on_path(v3, v0) = v7 & $i(v9) & ( ~ (v6 = 0) | (v8 = % 70.11/10.02 | 0 & v7 = 0 & ( ~ (v5 = 0) | ( ! [v12: $i] : ( ~ (precedes(v12, % 70.11/10.02 | v4, v0) = 0) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 % 70.11/10.02 | = 0) & sequential(v3, v12) = v13)) & ! [v12: $i] : % 70.11/10.02 | ( ~ (sequential(v3, v12) = 0) | ~ $i(v12) | ? [v13: int] % 70.11/10.02 | : ( ~ (v13 = 0) & precedes(v12, v4, v0) = v13)))) & (v5 % 70.11/10.02 | = 0 | (v11 = 0 & v10 = 0 & precedes(v9, v4, v0) = 0 & % 70.11/10.02 | sequential(v3, v9) = 0)))))) % 70.11/10.02 | % 70.11/10.02 | ALPHA: (shortest_path_defn) implies: % 70.11/10.02 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, % 70.11/10.02 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 70.11/10.02 | (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & ! [v4: $i] : % 70.11/10.02 | ! [v5: $i] : ( ~ (length_of(v4) = v5) | ~ $i(v4) | ? [v6: any] : % 70.11/10.02 | ? [v7: any] : (less_or_equal(v3, v5) = v7 & path(v0, v1, v4) = % 70.11/10.02 | v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4: $i] : ( ~ (path(v0, % 70.11/10.02 | v1, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (length_of(v4) = v5 % 70.11/10.02 | & less_or_equal(v3, v5) = 0 & $i(v5))))) % 70.11/10.02 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (path(v0, v1, % 70.11/10.02 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 70.11/10.02 | [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] % 70.11/10.02 | : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v3 & $i(v5) & % 70.11/10.02 | $i(v3) & (v4 = 0 | (v6 = 0 & ~ (v8 = 0) & length_of(v5) = v7 & % 70.11/10.02 | less_or_equal(v3, v7) = v8 & path(v0, v1, v5) = 0 & $i(v7))))) % 70.11/10.02 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (path(v0, % 70.11/10.02 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 70.11/10.02 | : ? [v5: $i] : (shortest_path(v0, v1, v2) = v4 & length_of(v2) = v5 % 70.11/10.02 | & $i(v5) & ( ~ (v4 = 0) | (v3 = 0 & ~ (v1 = v0) & ! [v6: $i] : % 70.11/10.02 | ! [v7: $i] : ( ~ (length_of(v6) = v7) | ~ $i(v6) | ? [v8: % 70.11/10.02 | any] : ? [v9: any] : (less_or_equal(v5, v7) = v9 & % 70.11/10.02 | path(v0, v1, v6) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v6: % 70.11/10.02 | $i] : ( ~ (path(v0, v1, v6) = 0) | ~ $i(v6) | ? [v7: $i] : % 70.11/10.02 | (length_of(v6) = v7 & less_or_equal(v5, v7) = 0 & % 70.11/10.02 | $i(v7))))))) % 70.11/10.02 | % 70.11/10.02 | ALPHA: (shortest_path_properties) implies: % 70.11/10.03 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.03 | ! [v5: any] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v3, % 70.11/10.03 | v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 70.11/10.03 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (precedes(v2, % 70.11/10.03 | v3, v4) = v6 & head_of(v3) = v8 & tail_of(v2) = v7 & $i(v8) & % 70.11/10.03 | $i(v7) & ( ~ (v6 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ % 70.11/10.03 | (head_of(v9) = v8) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 70.11/10.03 | v7) & tail_of(v9) = v10 & $i(v10))) & ! [v9: $i] : ( ~ % 70.11/10.03 | (tail_of(v9) = v7) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 70.11/10.03 | v8) & head_of(v9) = v10 & $i(v10))))))) % 70.11/10.03 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.11/10.03 | ! [v5: $i] : ! [v6: $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ % 70.11/10.03 | (head_of(v3) = v6) | ~ (tail_of(v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 70.11/10.03 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 70.11/10.03 | (precedes(v3, v2, v4) = v8 & precedes(v2, v3, v4) = v7 & ( ~ (v7 = % 70.11/10.03 | 0) | ( ~ (v8 = 0) & ! [v9: $i] : ( ~ (head_of(v9) = v6) | ~ % 70.11/10.03 | $i(v9) | ? [v10: $i] : ( ~ (v10 = v5) & tail_of(v9) = v10 & % 70.11/10.03 | $i(v10))) & ! [v9: $i] : ( ~ (tail_of(v9) = v5) | ~ % 70.11/10.03 | $i(v9) | ? [v10: $i] : ( ~ (v10 = v6) & head_of(v9) = v10 & % 70.11/10.03 | $i(v10))))))) % 70.11/10.03 | % 70.11/10.03 | ALPHA: (path_length_sequential_pairs) implies: % 70.11/10.03 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 70.11/10.03 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 70.11/10.03 | (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 70.11/10.03 | length_of(v2) = v4 & $i(v4) & $i(v3))) % 70.11/10.03 | % 70.11/10.03 | ALPHA: (sequential_pairs_and_triangles) implies: % 70.11/10.04 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v1, v2, v0) = 0) | % 70.11/10.04 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 70.11/10.04 | [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ? [v9: int] % 70.11/10.04 | : ($i(v6) & $i(v5) & ((v9 = 0 & v8 = 0 & v7 = 0 & sequential(v5, v6) % 70.11/10.04 | = 0 & on_path(v6, v0) = 0 & on_path(v5, v0) = 0 & ! [v10: $i] % 70.11/10.04 | : ( ~ (triangle(v5, v6, v10) = 0) | ~ $i(v10))) | (v4 = v3 & % 70.11/10.04 | number_of_in(triangles, v0) = v3 & % 70.11/10.04 | number_of_in(sequential_pairs, v0) = v3 & $i(v3))))) % 70.11/10.04 | % 70.11/10.04 | ALPHA: (graph_has_them_all) implies: % 70.11/10.04 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (number_of_in(v0, v1) = % 70.11/10.04 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(v0, % 70.11/10.04 | graph) = v3 & less_or_equal(v2, v3) = 0 & $i(v3))) % 70.11/10.04 | % 70.11/10.04 | ALPHA: (maximal_path_length) implies: % 70.11/10.04 | (23) $i(triangles) % 70.11/10.04 | (24) $i(graph) % 70.11/10.04 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 70.11/10.04 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & minus(v4, n1) = v5 & % 70.11/10.04 | number_of_in(triangles, graph) = v0 & shortest_path(v2, v3, v1) = 0 % 70.11/10.04 | & length_of(v1) = v4 & less_or_equal(v5, v0) = v6 & $i(v5) & $i(v4) % 70.11/10.04 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & complete) % 70.11/10.04 | % 70.11/10.04 | ALPHA: (function-axioms) implies: % 70.11/10.04 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = % 70.11/10.04 | v1) | ~ (tail_of(v2) = v0)) % 70.11/10.04 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.04 | : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) % 70.11/10.04 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = % 70.11/10.04 | v1) | ~ (head_of(v2) = v0)) % 70.11/10.04 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.04 | : (v1 = v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) % 70.11/10.04 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) % 70.11/10.04 | = v1) | ~ (length_of(v2) = v0)) % 70.11/10.04 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.04 | : ! [v3: $i] : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, % 70.11/10.04 | v2) = v0)) % 70.11/10.04 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.04 | : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 70.11/10.04 | (less_or_equal(v3, v2) = v0)) % 70.11/10.04 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.11/10.04 | (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0)) % 70.11/10.04 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.11/10.04 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 70.11/10.04 | (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.04 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (path(v4, v3, v2) = v1) | % 70.11/10.04 | ~ (path(v4, v3, v2) = v0)) % 70.11/10.05 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.05 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = % 70.11/10.05 | v1) | ~ (precedes(v4, v3, v2) = v0)) % 70.11/10.05 | (37) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 70.11/10.05 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (shortest_path(v4, v3, v2) % 70.11/10.05 | = v1) | ~ (shortest_path(v4, v3, v2) = v0)) % 70.11/10.05 | % 70.11/10.05 | DELTA: instantiating (25) with fresh symbols all_20_0, all_20_1, all_20_2, % 70.11/10.05 | all_20_3, all_20_4, all_20_5, all_20_6 gives: % 70.11/10.05 | (38) ~ (all_20_0 = 0) & minus(all_20_2, n1) = all_20_1 & % 70.11/10.05 | number_of_in(triangles, graph) = all_20_6 & shortest_path(all_20_4, % 70.11/10.05 | all_20_3, all_20_5) = 0 & length_of(all_20_5) = all_20_2 & % 70.11/10.05 | less_or_equal(all_20_1, all_20_6) = all_20_0 & $i(all_20_1) & % 70.11/10.05 | $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & % 70.11/10.05 | $i(all_20_6) & complete % 70.11/10.05 | % 70.11/10.05 | ALPHA: (38) implies: % 70.11/10.05 | (39) ~ (all_20_0 = 0) % 70.11/10.05 | (40) complete % 70.11/10.05 | (41) $i(all_20_5) % 70.11/10.05 | (42) $i(all_20_4) % 70.11/10.05 | (43) $i(all_20_3) % 70.11/10.05 | (44) less_or_equal(all_20_1, all_20_6) = all_20_0 % 70.11/10.05 | (45) length_of(all_20_5) = all_20_2 % 70.11/10.05 | (46) shortest_path(all_20_4, all_20_3, all_20_5) = 0 % 70.11/10.05 | (47) number_of_in(triangles, graph) = all_20_6 % 70.11/10.05 | (48) minus(all_20_2, n1) = all_20_1 % 70.11/10.05 | % 70.11/10.05 | BETA: splitting (complete_properties) gives: % 70.11/10.05 | % 70.11/10.05 | Case 1: % 70.11/10.05 | | % 70.11/10.05 | | (49) ~ complete % 70.11/10.05 | | % 70.11/10.05 | | PRED_UNIFY: (40), (49) imply: % 70.11/10.05 | | (50) $false % 70.11/10.05 | | % 70.11/10.05 | | CLOSE: (50) is inconsistent. % 70.11/10.05 | | % 70.11/10.05 | Case 2: % 70.11/10.05 | | % 70.11/10.05 | | (51) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vertex(v1) = 0) | ~ % 70.11/10.05 | | (vertex(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 70.11/10.05 | | $i] : ? [v4: $i] : (head_of(v2) = v3 & edge(v2) = 0 & % 70.11/10.05 | | tail_of(v2) = v4 & $i(v4) & $i(v3) & $i(v2) & ((v4 = v1 & v3 = % 70.11/10.05 | | v0) | (v4 = v0 & v3 = v1)))) % 70.11/10.05 | | % 70.11/10.05 | | BETA: splitting (sequential_is_triangle) gives: % 70.11/10.05 | | % 70.11/10.05 | | Case 1: % 70.11/10.05 | | | % 70.11/10.05 | | | (52) ~ complete % 70.11/10.05 | | | % 70.11/10.05 | | | PRED_UNIFY: (40), (52) imply: % 70.11/10.05 | | | (53) $false % 70.11/10.05 | | | % 70.11/10.05 | | | CLOSE: (53) is inconsistent. % 70.11/10.05 | | | % 70.11/10.05 | | Case 2: % 70.11/10.05 | | | % 70.11/10.06 | | | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 70.11/10.06 | | | $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (precedes(v2, v3, % 70.11/10.06 | | | v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 70.11/10.06 | | | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ($i(v6) & % 70.11/10.06 | | | ((v7 = 0 & triangle(v2, v3, v6) = 0) | ( ~ (v5 = 0) & % 70.11/10.06 | | | sequential(v2, v3) = v5)))) & ! [v0: $i] : ! [v1: $i] : % 70.11/10.06 | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (shortest_path(v0, % 70.11/10.06 | | | v1, v4) = 0) | ~ (sequential(v2, v3) = 0) | ~ $i(v4) | ~ % 70.11/10.06 | | | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? % 70.11/10.06 | | | [v6: $i] : ? [v7: int] : ($i(v6) & ((v7 = 0 & triangle(v2, v3, % 70.11/10.06 | | | v6) = 0) | ( ~ (v5 = 0) & precedes(v2, v3, v4) = v5)))) % 70.11/10.06 | | | % 70.11/10.06 | | | ALPHA: (54) implies: % 70.11/10.06 | | | (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 70.11/10.06 | | | $i] : ( ~ (shortest_path(v0, v1, v4) = 0) | ~ (sequential(v2, % 70.11/10.06 | | | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 70.11/10.06 | | | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ($i(v6) & % 70.11/10.06 | | | ((v7 = 0 & triangle(v2, v3, v6) = 0) | ( ~ (v5 = 0) & % 70.11/10.06 | | | precedes(v2, v3, v4) = v5)))) % 70.11/10.06 | | | % 70.11/10.06 | | | GROUND_INST: instantiating (15) with all_20_4, all_20_3, all_20_5, % 70.11/10.06 | | | simplifying with (41), (42), (43), (46) gives: % 70.11/10.06 | | | (56) ? [v0: $i] : (length_of(all_20_5) = v0 & path(all_20_4, all_20_3, % 70.11/10.06 | | | all_20_5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 70.11/10.06 | | | (length_of(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] % 70.11/10.06 | | | : (less_or_equal(v0, v2) = v4 & path(all_20_4, all_20_3, v1) = % 70.11/10.06 | | | v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ % 70.11/10.06 | | | (path(all_20_4, all_20_3, v1) = 0) | ~ $i(v1) | ? [v2: $i] : % 70.11/10.06 | | | (length_of(v1) = v2 & less_or_equal(v0, v2) = 0 & $i(v2)))) % 70.11/10.06 | | | % 70.11/10.06 | | | GROUND_INST: instantiating (22) with triangles, graph, all_20_6, % 70.11/10.06 | | | simplifying with (23), (24), (47) gives: % 70.11/10.06 | | | (57) ? [v0: $i] : (number_of_in(triangles, graph) = v0 & % 70.11/10.06 | | | less_or_equal(all_20_6, v0) = 0 & $i(v0)) % 70.11/10.06 | | | % 70.11/10.06 | | | DELTA: instantiating (57) with fresh symbol all_36_0 gives: % 70.11/10.06 | | | (58) number_of_in(triangles, graph) = all_36_0 & % 70.11/10.06 | | | less_or_equal(all_20_6, all_36_0) = 0 & $i(all_36_0) % 70.11/10.06 | | | % 70.11/10.06 | | | ALPHA: (58) implies: % 70.11/10.06 | | | (59) number_of_in(triangles, graph) = all_36_0 % 70.11/10.06 | | | % 70.11/10.06 | | | DELTA: instantiating (56) with fresh symbol all_38_0 gives: % 70.11/10.06 | | | (60) length_of(all_20_5) = all_38_0 & path(all_20_4, all_20_3, % 70.11/10.06 | | | all_20_5) = 0 & $i(all_38_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.11/10.06 | | | (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 70.11/10.06 | | | (less_or_equal(all_38_0, v1) = v3 & path(all_20_4, all_20_3, v0) % 70.11/10.06 | | | = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 70.11/10.06 | | | (path(all_20_4, all_20_3, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 70.11/10.06 | | | (length_of(v0) = v1 & less_or_equal(all_38_0, v1) = 0 & $i(v1))) % 70.11/10.06 | | | % 70.11/10.06 | | | ALPHA: (60) implies: % 70.11/10.06 | | | (61) path(all_20_4, all_20_3, all_20_5) = 0 % 70.11/10.06 | | | (62) length_of(all_20_5) = all_38_0 % 70.11/10.06 | | | (63) ! [v0: $i] : ! [v1: $i] : ( ~ (length_of(v0) = v1) | ~ $i(v0) | % 70.11/10.06 | | | ? [v2: any] : ? [v3: any] : (less_or_equal(all_38_0, v1) = v3 % 70.11/10.06 | | | & path(all_20_4, all_20_3, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 70.11/10.06 | | | % 70.11/10.06 | | | GROUND_INST: instantiating (63) with all_20_5, all_20_2, simplifying with % 70.11/10.06 | | | (41), (45) gives: % 70.11/10.06 | | | (64) ? [v0: any] : ? [v1: any] : (less_or_equal(all_38_0, all_20_2) = % 70.11/10.06 | | | v1 & path(all_20_4, all_20_3, all_20_5) = v0 & ( ~ (v0 = 0) | v1 % 70.11/10.06 | | | = 0)) % 70.11/10.06 | | | % 70.11/10.06 | | | DELTA: instantiating (64) with fresh symbols all_41_0, all_41_1 gives: % 70.11/10.06 | | | (65) less_or_equal(all_38_0, all_20_2) = all_41_0 & path(all_20_4, % 70.11/10.06 | | | all_20_3, all_20_5) = all_41_1 & ( ~ (all_41_1 = 0) | all_41_0 = % 70.11/10.06 | | | 0) % 70.11/10.06 | | | % 70.11/10.06 | | | ALPHA: (65) implies: % 70.11/10.06 | | | (66) path(all_20_4, all_20_3, all_20_5) = all_41_1 % 70.11/10.06 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (35) with 0, all_41_1, all_20_5, all_20_3, % 70.11/10.07 | | | all_20_4, simplifying with (61), (66) gives: % 70.11/10.07 | | | (67) all_41_1 = 0 % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (30) with all_20_2, all_38_0, all_20_5, % 70.11/10.07 | | | simplifying with (45), (62) gives: % 70.11/10.07 | | | (68) all_38_0 = all_20_2 % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (33) with all_20_6, all_36_0, graph, triangles, % 70.11/10.07 | | | simplifying with (47), (59) gives: % 70.11/10.07 | | | (69) all_36_0 = all_20_6 % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (16) with all_20_4, all_20_3, all_20_5, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (70) all_20_3 = all_20_4 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 70.11/10.07 | | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 70.11/10.07 | | | (shortest_path(all_20_4, all_20_3, all_20_5) = v1 & % 70.11/10.07 | | | length_of(all_20_5) = v0 & $i(v2) & $i(v0) & (v1 = 0 | (v3 = 0 & % 70.11/10.07 | | | ~ (v5 = 0) & length_of(v2) = v4 & less_or_equal(v0, v4) = % 70.11/10.07 | | | v5 & path(all_20_4, all_20_3, v2) = 0 & $i(v4)))) % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (21) with all_20_5, all_20_4, all_20_3, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 70.11/10.07 | | | int] : ? [v5: int] : ? [v6: int] : ($i(v3) & $i(v2) & ((v6 = 0 % 70.11/10.07 | | | & v5 = 0 & v4 = 0 & sequential(v2, v3) = 0 & on_path(v3, % 70.11/10.07 | | | all_20_5) = 0 & on_path(v2, all_20_5) = 0 & ! [v7: $i] : % 70.11/10.07 | | | ( ~ (triangle(v2, v3, v7) = 0) | ~ $i(v7))) | (v1 = v0 & % 70.11/10.07 | | | number_of_in(triangles, all_20_5) = v0 & % 70.11/10.07 | | | number_of_in(sequential_pairs, all_20_5) = v0 & $i(v0)))) % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (8) with all_20_4, all_20_3, all_20_5, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 70.11/10.07 | | | int] : ? [v5: int] : (path_cons(v0, empty) = v2 & head_of(v0) = % 70.11/10.07 | | | v1 & edge(v0) = 0 & tail_of(v0) = all_20_4 & $i(v3) & $i(v2) & % 70.11/10.07 | | | $i(v1) & $i(v0) & ( ~ (v2 = all_20_5) | ~ (v1 = all_20_3) | ( ! % 70.11/10.07 | | | [v6: $i] : ( ~ (path_cons(v0, v6) = all_20_5) | ~ $i(v6) | % 70.11/10.07 | | | ? [v7: int] : ( ~ (v7 = 0) & path(all_20_3, all_20_3, v6) % 70.11/10.07 | | | = v7)) & ! [v6: $i] : ( ~ (path(all_20_3, all_20_3, v6) % 70.11/10.07 | | | = 0) | ~ $i(v6) | ? [v7: any] : ( ~ (v7 = all_20_5) & % 70.11/10.07 | | | path_cons(v0, v6) = v7 & $i(v7))))) & ((v5 = all_20_5 & % 70.11/10.07 | | | v4 = 0 & path_cons(v0, v3) = all_20_5 & path(v1, all_20_3, % 70.11/10.07 | | | v3) = 0) | (v2 = all_20_5 & v1 = all_20_3))) % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (20) with all_20_4, all_20_3, all_20_5, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (73) ? [v0: $i] : ? [v1: $i] : (minus(v1, n1) = v0 & % 70.11/10.07 | | | number_of_in(sequential_pairs, all_20_5) = v0 & % 70.11/10.07 | | | length_of(all_20_5) = v1 & $i(v1) & $i(v0)) % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (7) with all_20_4, all_20_3, all_20_5, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (74) vertex(all_20_3) = 0 & vertex(all_20_4) = 0 % 70.11/10.07 | | | % 70.11/10.07 | | | ALPHA: (74) implies: % 70.11/10.07 | | | (75) vertex(all_20_4) = 0 % 70.11/10.07 | | | (76) vertex(all_20_3) = 0 % 70.11/10.07 | | | % 70.11/10.07 | | | GROUND_INST: instantiating (17) with all_20_4, all_20_3, all_20_5, 0, % 70.11/10.07 | | | simplifying with (41), (42), (43), (61) gives: % 70.11/10.07 | | | (77) ? [v0: any] : ? [v1: $i] : (shortest_path(all_20_4, all_20_3, % 70.11/10.07 | | | all_20_5) = v0 & length_of(all_20_5) = v1 & $i(v1) & ( ~ (v0 = % 70.11/10.07 | | | 0) | ( ~ (all_20_3 = all_20_4) & ! [v2: $i] : ! [v3: $i] : % 70.11/10.07 | | | ( ~ (length_of(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 70.11/10.07 | | | [v5: any] : (less_or_equal(v1, v3) = v5 & path(all_20_4, % 70.11/10.07 | | | all_20_3, v2) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! % 70.11/10.07 | | | [v2: $i] : ( ~ (path(all_20_4, all_20_3, v2) = 0) | ~ % 70.11/10.07 | | | $i(v2) | ? [v3: $i] : (length_of(v2) = v3 & % 70.11/10.07 | | | less_or_equal(v1, v3) = 0 & $i(v3)))))) % 70.11/10.07 | | | % 70.11/10.07 | | | DELTA: instantiating (73) with fresh symbols all_59_0, all_59_1 gives: % 70.11/10.08 | | | (78) minus(all_59_0, n1) = all_59_1 & number_of_in(sequential_pairs, % 70.11/10.08 | | | all_20_5) = all_59_1 & length_of(all_20_5) = all_59_0 & % 70.11/10.08 | | | $i(all_59_0) & $i(all_59_1) % 70.11/10.08 | | | % 70.11/10.08 | | | ALPHA: (78) implies: % 70.11/10.08 | | | (79) length_of(all_20_5) = all_59_0 % 70.11/10.08 | | | (80) number_of_in(sequential_pairs, all_20_5) = all_59_1 % 70.11/10.08 | | | (81) minus(all_59_0, n1) = all_59_1 % 70.11/10.08 | | | % 70.11/10.08 | | | DELTA: instantiating (71) with fresh symbols all_61_0, all_61_1, all_61_2, % 70.11/10.08 | | | all_61_3, all_61_4, all_61_5, all_61_6 gives: % 70.11/10.08 | | | (82) $i(all_61_3) & $i(all_61_4) & ((all_61_0 = 0 & all_61_1 = 0 & % 70.11/10.08 | | | all_61_2 = 0 & sequential(all_61_4, all_61_3) = 0 & % 70.11/10.08 | | | on_path(all_61_3, all_20_5) = 0 & on_path(all_61_4, all_20_5) % 70.11/10.08 | | | = 0 & ! [v0: $i] : ( ~ (triangle(all_61_4, all_61_3, v0) = 0) % 70.11/10.08 | | | | ~ $i(v0))) | (all_61_5 = all_61_6 & % 70.11/10.08 | | | number_of_in(triangles, all_20_5) = all_61_6 & % 70.11/10.08 | | | number_of_in(sequential_pairs, all_20_5) = all_61_6 & % 70.11/10.08 | | | $i(all_61_6))) % 70.11/10.08 | | | % 70.11/10.08 | | | ALPHA: (82) implies: % 70.11/10.08 | | | (83) $i(all_61_4) % 70.11/10.08 | | | (84) $i(all_61_3) % 70.11/10.08 | | | (85) (all_61_0 = 0 & all_61_1 = 0 & all_61_2 = 0 & sequential(all_61_4, % 70.11/10.08 | | | all_61_3) = 0 & on_path(all_61_3, all_20_5) = 0 & % 70.11/10.08 | | | on_path(all_61_4, all_20_5) = 0 & ! [v0: $i] : ( ~ % 70.11/10.08 | | | (triangle(all_61_4, all_61_3, v0) = 0) | ~ $i(v0))) | % 70.11/10.08 | | | (all_61_5 = all_61_6 & number_of_in(triangles, all_20_5) = % 70.11/10.08 | | | all_61_6 & number_of_in(sequential_pairs, all_20_5) = all_61_6 & % 70.11/10.08 | | | $i(all_61_6)) % 70.11/10.08 | | | % 70.11/10.08 | | | DELTA: instantiating (77) with fresh symbols all_63_0, all_63_1 gives: % 70.11/10.08 | | | (86) shortest_path(all_20_4, all_20_3, all_20_5) = all_63_1 & % 70.11/10.08 | | | length_of(all_20_5) = all_63_0 & $i(all_63_0) & ( ~ (all_63_1 = 0) % 70.11/10.08 | | | | ( ~ (all_20_3 = all_20_4) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.11/10.08 | | | (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 70.11/10.08 | | | any] : (less_or_equal(all_63_0, v1) = v3 & path(all_20_4, % 70.11/10.08 | | | all_20_3, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: % 70.11/10.08 | | | $i] : ( ~ (path(all_20_4, all_20_3, v0) = 0) | ~ $i(v0) | % 70.11/10.08 | | | ? [v1: $i] : (length_of(v0) = v1 & less_or_equal(all_63_0, % 70.11/10.08 | | | v1) = 0 & $i(v1))))) % 70.11/10.08 | | | % 70.11/10.08 | | | ALPHA: (86) implies: % 70.11/10.08 | | | (87) shortest_path(all_20_4, all_20_3, all_20_5) = all_63_1 % 70.11/10.08 | | | (88) ~ (all_63_1 = 0) | ( ~ (all_20_3 = all_20_4) & ! [v0: $i] : ! % 70.11/10.08 | | | [v1: $i] : ( ~ (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 70.11/10.08 | | | ? [v3: any] : (less_or_equal(all_63_0, v1) = v3 & % 70.11/10.08 | | | path(all_20_4, all_20_3, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 70.11/10.08 | | | & ! [v0: $i] : ( ~ (path(all_20_4, all_20_3, v0) = 0) | ~ % 70.11/10.08 | | | $i(v0) | ? [v1: $i] : (length_of(v0) = v1 & % 70.11/10.08 | | | less_or_equal(all_63_0, v1) = 0 & $i(v1)))) % 70.11/10.08 | | | % 70.11/10.08 | | | DELTA: instantiating (72) with fresh symbols all_65_0, all_65_1, all_65_2, % 70.11/10.08 | | | all_65_3, all_65_4, all_65_5 gives: % 70.11/10.08 | | | (89) path_cons(all_65_5, empty) = all_65_3 & head_of(all_65_5) = % 70.11/10.08 | | | all_65_4 & edge(all_65_5) = 0 & tail_of(all_65_5) = all_20_4 & % 70.11/10.08 | | | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) & ( ~ % 70.11/10.08 | | | (all_65_3 = all_20_5) | ~ (all_65_4 = all_20_3) | ( ! [v0: $i] % 70.11/10.08 | | | : ( ~ (path_cons(all_65_5, v0) = all_20_5) | ~ $i(v0) | ? % 70.11/10.08 | | | [v1: int] : ( ~ (v1 = 0) & path(all_20_3, all_20_3, v0) = % 70.11/10.08 | | | v1)) & ! [v0: $i] : ( ~ (path(all_20_3, all_20_3, v0) = % 70.11/10.08 | | | 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_20_5) & % 70.11/10.08 | | | path_cons(all_65_5, v0) = v1 & $i(v1))))) & ((all_65_0 = % 70.11/10.08 | | | all_20_5 & all_65_1 = 0 & path_cons(all_65_5, all_65_2) = % 70.11/10.08 | | | all_20_5 & path(all_65_4, all_20_3, all_65_2) = 0) | (all_65_3 % 70.11/10.08 | | | = all_20_5 & all_65_4 = all_20_3)) % 70.11/10.08 | | | % 70.11/10.08 | | | ALPHA: (89) implies: % 70.11/10.08 | | | (90) $i(all_65_5) % 70.11/10.08 | | | (91) $i(all_65_3) % 70.11/10.08 | | | (92) tail_of(all_65_5) = all_20_4 % 70.11/10.08 | | | (93) edge(all_65_5) = 0 % 70.11/10.08 | | | (94) head_of(all_65_5) = all_65_4 % 70.11/10.08 | | | (95) (all_65_0 = all_20_5 & all_65_1 = 0 & path_cons(all_65_5, % 70.11/10.08 | | | all_65_2) = all_20_5 & path(all_65_4, all_20_3, all_65_2) = 0) % 70.11/10.08 | | | | (all_65_3 = all_20_5 & all_65_4 = all_20_3) % 70.11/10.08 | | | (96) ~ (all_65_3 = all_20_5) | ~ (all_65_4 = all_20_3) | ( ! [v0: $i] % 70.11/10.08 | | | : ( ~ (path_cons(all_65_5, v0) = all_20_5) | ~ $i(v0) | ? [v1: % 70.11/10.08 | | | int] : ( ~ (v1 = 0) & path(all_20_3, all_20_3, v0) = v1)) & % 70.11/10.08 | | | ! [v0: $i] : ( ~ (path(all_20_3, all_20_3, v0) = 0) | ~ $i(v0) % 70.11/10.08 | | | | ? [v1: any] : ( ~ (v1 = all_20_5) & path_cons(all_65_5, v0) % 70.11/10.08 | | | = v1 & $i(v1)))) % 70.11/10.08 | | | % 70.11/10.08 | | | GROUND_INST: instantiating (30) with all_20_2, all_59_0, all_20_5, % 70.11/10.08 | | | simplifying with (45), (79) gives: % 70.11/10.08 | | | (97) all_59_0 = all_20_2 % 70.11/10.08 | | | % 70.11/10.09 | | | GROUND_INST: instantiating (37) with 0, all_63_1, all_20_5, all_20_3, % 70.11/10.09 | | | all_20_4, simplifying with (46), (87) gives: % 70.11/10.09 | | | (98) all_63_1 = 0 % 70.11/10.09 | | | % 70.11/10.09 | | | REDUCE: (81), (97) imply: % 70.11/10.09 | | | (99) minus(all_20_2, n1) = all_59_1 % 70.11/10.09 | | | % 70.11/10.09 | | | BETA: splitting (88) gives: % 70.11/10.09 | | | % 70.11/10.09 | | | Case 1: % 70.11/10.09 | | | | % 70.11/10.09 | | | | (100) ~ (all_63_1 = 0) % 70.11/10.09 | | | | % 70.11/10.09 | | | | REDUCE: (98), (100) imply: % 70.11/10.09 | | | | (101) $false % 70.11/10.09 | | | | % 70.11/10.09 | | | | CLOSE: (101) is inconsistent. % 70.11/10.09 | | | | % 70.11/10.09 | | | Case 2: % 70.11/10.09 | | | | % 70.11/10.09 | | | | (102) ~ (all_20_3 = all_20_4) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.11/10.09 | | | | (length_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 70.11/10.09 | | | | any] : (less_or_equal(all_63_0, v1) = v3 & path(all_20_4, % 70.11/10.09 | | | | all_20_3, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: % 70.11/10.09 | | | | $i] : ( ~ (path(all_20_4, all_20_3, v0) = 0) | ~ $i(v0) | ? % 70.11/10.09 | | | | [v1: $i] : (length_of(v0) = v1 & less_or_equal(all_63_0, v1) % 70.11/10.09 | | | | = 0 & $i(v1))) % 70.11/10.09 | | | | % 70.11/10.09 | | | | ALPHA: (102) implies: % 70.11/10.09 | | | | (103) ~ (all_20_3 = all_20_4) % 70.11/10.09 | | | | % 70.11/10.09 | | | | BETA: splitting (70) gives: % 70.11/10.09 | | | | % 70.11/10.09 | | | | Case 1: % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | (104) all_20_3 = all_20_4 % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | REDUCE: (103), (104) imply: % 70.11/10.09 | | | | | (105) $false % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | CLOSE: (105) is inconsistent. % 70.11/10.09 | | | | | % 70.11/10.09 | | | | Case 2: % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | (106) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? % 70.11/10.09 | | | | | [v4: $i] : ? [v5: int] : (shortest_path(all_20_4, all_20_3, % 70.11/10.09 | | | | | all_20_5) = v1 & length_of(all_20_5) = v0 & $i(v2) & % 70.11/10.09 | | | | | $i(v0) & (v1 = 0 | (v3 = 0 & ~ (v5 = 0) & length_of(v2) = % 70.11/10.09 | | | | | v4 & less_or_equal(v0, v4) = v5 & path(all_20_4, % 70.11/10.09 | | | | | all_20_3, v2) = 0 & $i(v4)))) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | DELTA: instantiating (106) with fresh symbols all_80_0, all_80_1, % 70.11/10.09 | | | | | all_80_2, all_80_3, all_80_4, all_80_5 gives: % 70.11/10.09 | | | | | (107) shortest_path(all_20_4, all_20_3, all_20_5) = all_80_4 & % 70.11/10.09 | | | | | length_of(all_20_5) = all_80_5 & $i(all_80_3) & $i(all_80_5) % 70.11/10.09 | | | | | & (all_80_4 = 0 | (all_80_2 = 0 & ~ (all_80_0 = 0) & % 70.11/10.09 | | | | | length_of(all_80_3) = all_80_1 & less_or_equal(all_80_5, % 70.11/10.09 | | | | | all_80_1) = all_80_0 & path(all_20_4, all_20_3, % 70.11/10.09 | | | | | all_80_3) = 0 & $i(all_80_1))) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | ALPHA: (107) implies: % 70.11/10.09 | | | | | (108) shortest_path(all_20_4, all_20_3, all_20_5) = all_80_4 % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (37) with 0, all_80_4, all_20_5, all_20_3, % 70.11/10.09 | | | | | all_20_4, simplifying with (46), (108) gives: % 70.11/10.09 | | | | | (109) all_80_4 = 0 % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (34) with all_20_1, all_59_1, n1, all_20_2, % 70.11/10.09 | | | | | simplifying with (48), (99) gives: % 70.11/10.09 | | | | | (110) all_59_1 = all_20_1 % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | REDUCE: (80), (110) imply: % 70.11/10.09 | | | | | (111) number_of_in(sequential_pairs, all_20_5) = all_20_1 % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (5) with all_65_5, all_20_4, simplifying % 70.11/10.09 | | | | | with (90), (92) gives: % 70.11/10.09 | | | | | (112) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 70.11/10.09 | | | | | (vertex(v1) = v2 & vertex(all_20_4) = v3 & head_of(all_65_5) % 70.11/10.09 | | | | | = v1 & edge(all_65_5) = v0 & $i(v1) & ( ~ (v0 = 0) | (v3 = % 70.11/10.09 | | | | | 0 & v2 = 0))) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (2) with all_65_5, all_20_4, simplifying % 70.11/10.09 | | | | | with (90), (92) gives: % 70.11/10.09 | | | | | (113) ? [v0: any] : ? [v1: $i] : (head_of(all_65_5) = v1 & % 70.11/10.09 | | | | | edge(all_65_5) = v0 & $i(v1) & ( ~ (v1 = all_20_4) | ~ (v0 % 70.11/10.09 | | | | | = 0))) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (9) with all_20_4, all_20_3, all_20_5, % 70.11/10.09 | | | | | all_65_5, 0, simplifying with (41), (42), (43), (61), % 70.11/10.09 | | | | | (90), (93) gives: % 70.11/10.09 | | | | | (114) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 70.11/10.09 | | | | | [v4: any] : (on_path(all_65_5, all_20_5) = v0 & in_path(v3, % 70.11/10.09 | | | | | all_20_5) = v4 & in_path(v1, all_20_5) = v2 & % 70.11/10.09 | | | | | head_of(all_65_5) = v1 & tail_of(all_65_5) = v3 & $i(v3) & % 70.11/10.09 | | | | | $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0))) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (1) with all_65_5, simplifying with (90), % 70.11/10.09 | | | | | (93) gives: % 70.11/10.09 | | | | | (115) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & head_of(all_65_5) % 70.11/10.09 | | | | | = v0 & tail_of(all_65_5) = v1 & $i(v1) & $i(v0)) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (4) with all_65_5, simplifying with (90), % 70.11/10.09 | | | | | (93) gives: % 70.11/10.09 | | | | | (116) ? [v0: $i] : ? [v1: $i] : (vertex(v1) = 0 & vertex(v0) = 0 % 70.11/10.09 | | | | | & head_of(all_65_5) = v0 & tail_of(all_65_5) = v1 & $i(v1) % 70.11/10.09 | | | | | & $i(v0)) % 70.11/10.09 | | | | | % 70.11/10.09 | | | | | GROUND_INST: instantiating (19) with all_20_4, all_20_3, all_65_5, % 70.11/10.09 | | | | | all_65_5, all_20_5, all_20_4, all_65_4, simplifying with % 70.11/10.09 | | | | | (41), (42), (43), (46), (90), (92), (94) gives: % 70.11/10.10 | | | | | (117) ? [v0: any] : ? [v1: any] : (precedes(all_65_5, all_65_5, % 70.11/10.10 | | | | | all_20_5) = v1 & precedes(all_65_5, all_65_5, all_20_5) = % 70.11/10.10 | | | | | v0 & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ % 70.11/10.10 | | | | | (head_of(v2) = all_65_4) | ~ $i(v2) | ? [v3: any] : % 70.11/10.10 | | | | | ( ~ (v3 = all_20_4) & tail_of(v2) = v3 & $i(v3))) & % 70.11/10.10 | | | | | ! [v2: $i] : ( ~ (tail_of(v2) = all_20_4) | ~ $i(v2) | % 70.11/10.10 | | | | | ? [v3: any] : ( ~ (v3 = all_65_4) & head_of(v2) = v3 % 70.11/10.10 | | | | | & $i(v3)))))) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | GROUND_INST: instantiating (6) with all_65_5, all_65_4, simplifying % 70.11/10.10 | | | | | with (90), (94) gives: % 70.11/10.10 | | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 70.11/10.10 | | | | | (vertex(v2) = v3 & vertex(all_65_4) = v1 & edge(all_65_5) = % 70.11/10.10 | | | | | v0 & tail_of(all_65_5) = v2 & $i(v2) & ( ~ (v0 = 0) | (v3 = % 70.11/10.10 | | | | | 0 & v1 = 0))) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | GROUND_INST: instantiating (3) with all_65_5, all_65_4, simplifying % 70.11/10.10 | | | | | with (90), (94) gives: % 70.11/10.10 | | | | | (119) ? [v0: any] : ? [v1: $i] : (edge(all_65_5) = v0 & % 70.11/10.10 | | | | | tail_of(all_65_5) = v1 & $i(v1) & ( ~ (v1 = all_65_4) | ~ % 70.11/10.10 | | | | | (v0 = 0))) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | GROUND_INST: instantiating (51) with all_20_4, all_20_3, simplifying % 70.11/10.10 | | | | | with (42), (43), (75), (76) gives: % 70.11/10.10 | | | | | (120) all_20_3 = all_20_4 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 70.11/10.10 | | | | | : (head_of(v0) = v1 & edge(v0) = 0 & tail_of(v0) = v2 & % 70.11/10.10 | | | | | $i(v2) & $i(v1) & $i(v0) & ((v2 = all_20_3 & v1 = all_20_4) % 70.11/10.10 | | | | | | (v2 = all_20_4 & v1 = all_20_3))) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (119) with fresh symbols all_95_0, all_95_1 % 70.11/10.10 | | | | | gives: % 70.11/10.10 | | | | | (121) edge(all_65_5) = all_95_1 & tail_of(all_65_5) = all_95_0 & % 70.11/10.10 | | | | | $i(all_95_0) & ( ~ (all_95_0 = all_65_4) | ~ (all_95_1 = 0)) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (121) implies: % 70.11/10.10 | | | | | (122) $i(all_95_0) % 70.11/10.10 | | | | | (123) tail_of(all_65_5) = all_95_0 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (115) with fresh symbols all_97_0, all_97_1 % 70.11/10.10 | | | | | gives: % 70.11/10.10 | | | | | (124) ~ (all_97_0 = all_97_1) & head_of(all_65_5) = all_97_1 & % 70.11/10.10 | | | | | tail_of(all_65_5) = all_97_0 & $i(all_97_0) & $i(all_97_1) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (124) implies: % 70.11/10.10 | | | | | (125) ~ (all_97_0 = all_97_1) % 70.11/10.10 | | | | | (126) $i(all_97_1) % 70.11/10.10 | | | | | (127) tail_of(all_65_5) = all_97_0 % 70.11/10.10 | | | | | (128) head_of(all_65_5) = all_97_1 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (113) with fresh symbols all_99_0, all_99_1 % 70.11/10.10 | | | | | gives: % 70.11/10.10 | | | | | (129) head_of(all_65_5) = all_99_0 & edge(all_65_5) = all_99_1 & % 70.11/10.10 | | | | | $i(all_99_0) & ( ~ (all_99_0 = all_20_4) | ~ (all_99_1 = 0)) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (129) implies: % 70.11/10.10 | | | | | (130) head_of(all_65_5) = all_99_0 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (116) with fresh symbols all_101_0, all_101_1 % 70.11/10.10 | | | | | gives: % 70.11/10.10 | | | | | (131) vertex(all_101_0) = 0 & vertex(all_101_1) = 0 & % 70.11/10.10 | | | | | head_of(all_65_5) = all_101_1 & tail_of(all_65_5) = all_101_0 % 70.11/10.10 | | | | | & $i(all_101_0) & $i(all_101_1) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (131) implies: % 70.11/10.10 | | | | | (132) tail_of(all_65_5) = all_101_0 % 70.11/10.10 | | | | | (133) head_of(all_65_5) = all_101_1 % 70.11/10.10 | | | | | (134) vertex(all_101_1) = 0 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (112) with fresh symbols all_103_0, all_103_1, % 70.11/10.10 | | | | | all_103_2, all_103_3 gives: % 70.11/10.10 | | | | | (135) vertex(all_103_2) = all_103_1 & vertex(all_20_4) = all_103_0 % 70.11/10.10 | | | | | & head_of(all_65_5) = all_103_2 & edge(all_65_5) = all_103_3 % 70.11/10.10 | | | | | & $i(all_103_2) & ( ~ (all_103_3 = 0) | (all_103_0 = 0 & % 70.11/10.10 | | | | | all_103_1 = 0)) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (135) implies: % 70.11/10.10 | | | | | (136) head_of(all_65_5) = all_103_2 % 70.11/10.10 | | | | | (137) vertex(all_20_4) = all_103_0 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (118) with fresh symbols all_105_0, all_105_1, % 70.11/10.10 | | | | | all_105_2, all_105_3 gives: % 70.11/10.10 | | | | | (138) vertex(all_105_1) = all_105_0 & vertex(all_65_4) = all_105_2 % 70.11/10.10 | | | | | & edge(all_65_5) = all_105_3 & tail_of(all_65_5) = all_105_1 % 70.11/10.10 | | | | | & $i(all_105_1) & ( ~ (all_105_3 = 0) | (all_105_0 = 0 & % 70.11/10.10 | | | | | all_105_2 = 0)) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (138) implies: % 70.11/10.10 | | | | | (139) tail_of(all_65_5) = all_105_1 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (114) with fresh symbols all_107_0, all_107_1, % 70.11/10.10 | | | | | all_107_2, all_107_3, all_107_4 gives: % 70.11/10.10 | | | | | (140) on_path(all_65_5, all_20_5) = all_107_4 & in_path(all_107_1, % 70.11/10.10 | | | | | all_20_5) = all_107_0 & in_path(all_107_3, all_20_5) = % 70.11/10.10 | | | | | all_107_2 & head_of(all_65_5) = all_107_3 & tail_of(all_65_5) % 70.11/10.10 | | | | | = all_107_1 & $i(all_107_1) & $i(all_107_3) & ( ~ (all_107_4 % 70.11/10.10 | | | | | = 0) | (all_107_0 = 0 & all_107_2 = 0)) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (140) implies: % 70.11/10.10 | | | | | (141) tail_of(all_65_5) = all_107_1 % 70.11/10.10 | | | | | (142) head_of(all_65_5) = all_107_3 % 70.11/10.10 | | | | | (143) in_path(all_107_3, all_20_5) = all_107_2 % 70.11/10.10 | | | | | (144) in_path(all_107_1, all_20_5) = all_107_0 % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | DELTA: instantiating (117) with fresh symbols all_113_0, all_113_1 % 70.11/10.10 | | | | | gives: % 70.11/10.10 | | | | | (145) precedes(all_65_5, all_65_5, all_20_5) = all_113_0 & % 70.11/10.10 | | | | | precedes(all_65_5, all_65_5, all_20_5) = all_113_1 & ( ~ % 70.11/10.10 | | | | | (all_113_1 = 0) | ( ~ (all_113_0 = 0) & ! [v0: $i] : ( ~ % 70.11/10.10 | | | | | (head_of(v0) = all_65_4) | ~ $i(v0) | ? [v1: any] : ( % 70.11/10.10 | | | | | ~ (v1 = all_20_4) & tail_of(v0) = v1 & $i(v1))) & ! % 70.11/10.10 | | | | | [v0: $i] : ( ~ (tail_of(v0) = all_20_4) | ~ $i(v0) | ? % 70.11/10.10 | | | | | [v1: any] : ( ~ (v1 = all_65_4) & head_of(v0) = v1 & % 70.11/10.10 | | | | | $i(v1))))) % 70.11/10.10 | | | | | % 70.11/10.10 | | | | | ALPHA: (145) implies: % 70.11/10.10 | | | | | (146) precedes(all_65_5, all_65_5, all_20_5) = all_113_1 % 70.11/10.10 | | | | | (147) precedes(all_65_5, all_65_5, all_20_5) = all_113_0 % 70.11/10.11 | | | | | (148) ~ (all_113_1 = 0) | ( ~ (all_113_0 = 0) & ! [v0: $i] : ( ~ % 70.11/10.11 | | | | | (head_of(v0) = all_65_4) | ~ $i(v0) | ? [v1: any] : ( ~ % 70.11/10.11 | | | | | (v1 = all_20_4) & tail_of(v0) = v1 & $i(v1))) & ! [v0: % 70.11/10.11 | | | | | $i] : ( ~ (tail_of(v0) = all_20_4) | ~ $i(v0) | ? [v1: % 70.11/10.11 | | | | | any] : ( ~ (v1 = all_65_4) & head_of(v0) = v1 & % 70.11/10.11 | | | | | $i(v1)))) % 70.11/10.11 | | | | | % 70.11/10.11 | | | | | BETA: splitting (120) gives: % 70.11/10.11 | | | | | % 70.11/10.11 | | | | | Case 1: % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | (149) all_20_3 = all_20_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (103), (149) imply: % 70.11/10.11 | | | | | | (150) $false % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | CLOSE: (150) is inconsistent. % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | Case 2: % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | (151) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (head_of(v0) = v1 % 70.11/10.11 | | | | | | & edge(v0) = 0 & tail_of(v0) = v2 & $i(v2) & $i(v1) & % 70.11/10.11 | | | | | | $i(v0) & ((v2 = all_20_3 & v1 = all_20_4) | (v2 = % 70.11/10.11 | | | | | | all_20_4 & v1 = all_20_3))) % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | DELTA: instantiating (151) with fresh symbols all_119_0, all_119_1, % 70.11/10.11 | | | | | | all_119_2 gives: % 70.11/10.11 | | | | | | (152) head_of(all_119_2) = all_119_1 & edge(all_119_2) = 0 & % 70.11/10.11 | | | | | | tail_of(all_119_2) = all_119_0 & $i(all_119_0) & % 70.11/10.11 | | | | | | $i(all_119_1) & $i(all_119_2) & ((all_119_0 = all_20_3 & % 70.11/10.11 | | | | | | all_119_1 = all_20_4) | (all_119_0 = all_20_4 & % 70.11/10.11 | | | | | | all_119_1 = all_20_3)) % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | ALPHA: (152) implies: % 70.11/10.11 | | | | | | (153) $i(all_119_2) % 70.11/10.11 | | | | | | (154) tail_of(all_119_2) = all_119_0 % 70.11/10.11 | | | | | | (155) edge(all_119_2) = 0 % 70.11/10.11 | | | | | | (156) head_of(all_119_2) = all_119_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (26) with all_20_4, all_97_0, all_65_5, % 70.11/10.11 | | | | | | simplifying with (92), (127) gives: % 70.11/10.11 | | | | | | (157) all_97_0 = all_20_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (26) with all_101_0, all_105_1, all_65_5, % 70.11/10.11 | | | | | | simplifying with (132), (139) gives: % 70.11/10.11 | | | | | | (158) all_105_1 = all_101_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (26) with all_97_0, all_105_1, all_65_5, % 70.11/10.11 | | | | | | simplifying with (127), (139) gives: % 70.11/10.11 | | | | | | (159) all_105_1 = all_97_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (26) with all_105_1, all_107_1, all_65_5, % 70.11/10.11 | | | | | | simplifying with (139), (141) gives: % 70.11/10.11 | | | | | | (160) all_107_1 = all_105_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (26) with all_95_0, all_107_1, all_65_5, % 70.11/10.11 | | | | | | simplifying with (123), (141) gives: % 70.11/10.11 | | | | | | (161) all_107_1 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (28) with all_99_0, all_103_2, all_65_5, % 70.11/10.11 | | | | | | simplifying with (130), (136) gives: % 70.11/10.11 | | | | | | (162) all_103_2 = all_99_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (28) with all_65_4, all_107_3, all_65_5, % 70.11/10.11 | | | | | | simplifying with (94), (142) gives: % 70.11/10.11 | | | | | | (163) all_107_3 = all_65_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (28) with all_103_2, all_107_3, all_65_5, % 70.11/10.11 | | | | | | simplifying with (136), (142) gives: % 70.11/10.11 | | | | | | (164) all_107_3 = all_103_2 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (28) with all_101_1, all_107_3, all_65_5, % 70.11/10.11 | | | | | | simplifying with (133), (142) gives: % 70.11/10.11 | | | | | | (165) all_107_3 = all_101_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (28) with all_97_1, all_107_3, all_65_5, % 70.11/10.11 | | | | | | simplifying with (128), (142) gives: % 70.11/10.11 | | | | | | (166) all_107_3 = all_97_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (29) with 0, all_103_0, all_20_4, % 70.11/10.11 | | | | | | simplifying with (75), (137) gives: % 70.11/10.11 | | | | | | (167) all_103_0 = 0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | GROUND_INST: instantiating (36) with all_113_1, all_113_0, all_20_5, % 70.11/10.11 | | | | | | all_65_5, all_65_5, simplifying with (146), (147) % 70.11/10.11 | | | | | | gives: % 70.11/10.11 | | | | | | (168) all_113_0 = all_113_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (160), (161) imply: % 70.11/10.11 | | | | | | (169) all_105_1 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (169) implies: % 70.11/10.11 | | | | | | (170) all_105_1 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (165), (166) imply: % 70.11/10.11 | | | | | | (171) all_101_1 = all_97_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (164), (165) imply: % 70.11/10.11 | | | | | | (172) all_103_2 = all_101_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (172) implies: % 70.11/10.11 | | | | | | (173) all_103_2 = all_101_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (163), (165) imply: % 70.11/10.11 | | | | | | (174) all_101_1 = all_65_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (158), (170) imply: % 70.11/10.11 | | | | | | (175) all_101_0 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (158), (159) imply: % 70.11/10.11 | | | | | | (176) all_101_0 = all_97_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (162), (173) imply: % 70.11/10.11 | | | | | | (177) all_101_1 = all_99_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (177) implies: % 70.11/10.11 | | | | | | (178) all_101_1 = all_99_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (175), (176) imply: % 70.11/10.11 | | | | | | (179) all_97_0 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (179) implies: % 70.11/10.11 | | | | | | (180) all_97_0 = all_95_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (171), (178) imply: % 70.11/10.11 | | | | | | (181) all_99_0 = all_97_1 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (174), (178) imply: % 70.11/10.11 | | | | | | (182) all_99_0 = all_65_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (181), (182) imply: % 70.11/10.11 | | | | | | (183) all_97_1 = all_65_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (183) implies: % 70.11/10.11 | | | | | | (184) all_97_1 = all_65_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (157), (180) imply: % 70.11/10.11 | | | | | | (185) all_95_0 = all_20_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (185) implies: % 70.11/10.11 | | | | | | (186) all_95_0 = all_20_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | COMBINE_EQS: (161), (186) imply: % 70.11/10.11 | | | | | | (187) all_107_1 = all_20_4 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (125), (157), (184) imply: % 70.11/10.11 | | | | | | (188) ~ (all_65_4 = all_20_4) % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | SIMP: (188) implies: % 70.11/10.11 | | | | | | (189) ~ (all_65_4 = all_20_4) % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (144), (187) imply: % 70.11/10.11 | | | | | | (190) in_path(all_20_4, all_20_5) = all_107_0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (143), (163) imply: % 70.11/10.11 | | | | | | (191) in_path(all_65_4, all_20_5) = all_107_2 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (134), (174) imply: % 70.11/10.11 | | | | | | (192) vertex(all_65_4) = 0 % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | REDUCE: (126), (184) imply: % 70.11/10.11 | | | | | | (193) $i(all_65_4) % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | BETA: splitting (148) gives: % 70.11/10.11 | | | | | | % 70.11/10.11 | | | | | | Case 1: % 70.11/10.11 | | | | | | | % 70.11/10.11 | | | | | | | (194) ~ (all_113_1 = 0) % 70.11/10.11 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (19) with all_20_4, all_20_3, % 70.11/10.12 | | | | | | | all_119_2, all_65_5, all_20_5, all_119_0, all_65_4, % 70.11/10.12 | | | | | | | simplifying with (41), (42), (43), (46), (90), (94), % 70.11/10.12 | | | | | | | (153), (154) gives: % 70.11/10.12 | | | | | | | (195) ? [v0: any] : ? [v1: any] : (precedes(all_119_2, % 70.11/10.12 | | | | | | | all_65_5, all_20_5) = v0 & precedes(all_65_5, % 70.11/10.12 | | | | | | | all_119_2, all_20_5) = v1 & ( ~ (v0 = 0) | ( ~ (v1 = % 70.11/10.12 | | | | | | | 0) & ! [v2: $i] : ( ~ (head_of(v2) = all_65_4) | % 70.11/10.12 | | | | | | | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_119_0) & % 70.11/10.12 | | | | | | | tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( ~ % 70.11/10.12 | | | | | | | (tail_of(v2) = all_119_0) | ~ $i(v2) | ? [v3: % 70.11/10.12 | | | | | | | any] : ( ~ (v3 = all_65_4) & head_of(v2) = v3 & % 70.11/10.12 | | | | | | | $i(v3)))))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (5) with all_119_2, all_119_0, % 70.11/10.12 | | | | | | | simplifying with (153), (154) gives: % 70.11/10.12 | | | | | | | (196) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] % 70.11/10.12 | | | | | | | : (vertex(v1) = v2 & vertex(all_119_0) = v3 & % 70.11/10.12 | | | | | | | head_of(all_119_2) = v1 & edge(all_119_2) = v0 & $i(v1) % 70.11/10.12 | | | | | | | & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (19) with all_20_4, all_20_3, all_65_5, % 70.11/10.12 | | | | | | | all_119_2, all_20_5, all_20_4, all_119_1, simplifying % 70.11/10.12 | | | | | | | with (41), (42), (43), (46), (90), (92), (153), (156) % 70.11/10.12 | | | | | | | gives: % 70.11/10.12 | | | | | | | (197) ? [v0: any] : ? [v1: any] : (precedes(all_119_2, % 70.11/10.12 | | | | | | | all_65_5, all_20_5) = v1 & precedes(all_65_5, % 70.11/10.12 | | | | | | | all_119_2, all_20_5) = v0 & ( ~ (v0 = 0) | ( ~ (v1 = % 70.11/10.12 | | | | | | | 0) & ! [v2: $i] : ( ~ (head_of(v2) = all_119_1) % 70.11/10.12 | | | | | | | | ~ $i(v2) | ? [v3: any] : ( ~ (v3 = all_20_4) % 70.11/10.12 | | | | | | | & tail_of(v2) = v3 & $i(v3))) & ! [v2: $i] : ( % 70.11/10.12 | | | | | | | ~ (tail_of(v2) = all_20_4) | ~ $i(v2) | ? [v3: % 70.11/10.12 | | | | | | | any] : ( ~ (v3 = all_119_1) & head_of(v2) = v3 % 70.11/10.12 | | | | | | | & $i(v3)))))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (51) with all_20_4, all_65_4, % 70.11/10.12 | | | | | | | simplifying with (42), (75), (192), (193) gives: % 70.11/10.12 | | | | | | | (198) all_65_4 = all_20_4 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 70.11/10.12 | | | | | | | $i] : (head_of(v0) = v1 & edge(v0) = 0 & tail_of(v0) = % 70.11/10.12 | | | | | | | v2 & $i(v2) & $i(v1) & $i(v0) & ((v2 = all_65_4 & v1 = % 70.11/10.12 | | | | | | | all_20_4) | (v2 = all_20_4 & v1 = all_65_4))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (10) with all_20_4, all_20_3, all_20_5, % 70.11/10.12 | | | | | | | all_65_5, all_20_4, all_107_0, simplifying with (41), % 70.11/10.12 | | | | | | | (42), (43), (61), (90), (92), (190) gives: % 70.11/10.12 | | | | | | | (199) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] % 70.11/10.12 | | | | | | | : (on_path(all_65_5, all_20_5) = v0 & in_path(v2, % 70.11/10.12 | | | | | | | all_20_5) = v3 & head_of(all_65_5) = v2 & % 70.11/10.12 | | | | | | | edge(all_65_5) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 = 0 & % 70.11/10.12 | | | | | | | v1 = 0 & all_107_0 = 0))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (11) with all_20_4, all_20_3, all_20_5, % 70.11/10.12 | | | | | | | all_65_5, all_65_4, all_107_2, simplifying with (41), % 70.11/10.12 | | | | | | | (42), (43), (61), (90), (94), (191) gives: % 70.11/10.12 | | | | | | | (200) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] % 70.11/10.12 | | | | | | | : (on_path(all_65_5, all_20_5) = v0 & in_path(v2, % 70.11/10.12 | | | | | | | all_20_5) = v3 & edge(all_65_5) = v1 & % 70.11/10.12 | | | | | | | tail_of(all_65_5) = v2 & $i(v2) & ( ~ (v0 = 0) | (v3 = % 70.11/10.12 | | | | | | | 0 & v1 = 0 & all_107_2 = 0))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | GROUND_INST: instantiating (13) with all_20_5, all_20_4, all_20_3, % 70.11/10.12 | | | | | | | all_65_5, all_65_5, all_113_1, simplifying with (41), % 70.11/10.12 | | | | | | | (42), (43), (61), (90), (146) gives: % 70.11/10.12 | | | | | | | (201) all_113_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 70.11/10.12 | | | | | | | any] : (sequential(all_65_5, all_65_5) = v2 & % 70.11/10.12 | | | | | | | on_path(all_65_5, all_20_5) = v1 & on_path(all_65_5, % 70.11/10.12 | | | | | | | all_20_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v2 % 70.11/10.12 | | | | | | | = 0) & ! [v3: $i] : ( ~ (precedes(v3, all_65_5, % 70.11/10.12 | | | | | | | all_20_5) = 0) | ~ $i(v3) | ? [v4: int] : ( % 70.11/10.12 | | | | | | | ~ (v4 = 0) & sequential(all_65_5, v3) = v4)) & % 70.11/10.12 | | | | | | | ! [v3: $i] : ( ~ (sequential(all_65_5, v3) = 0) | % 70.11/10.12 | | | | | | | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 70.11/10.12 | | | | | | | precedes(v3, all_65_5, all_20_5) = v4))))) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | DELTA: instantiating (196) with fresh symbols all_154_0, % 70.11/10.12 | | | | | | | all_154_1, all_154_2, all_154_3 gives: % 70.11/10.12 | | | | | | | (202) vertex(all_154_2) = all_154_1 & vertex(all_119_0) = % 70.11/10.12 | | | | | | | all_154_0 & head_of(all_119_2) = all_154_2 & % 70.11/10.12 | | | | | | | edge(all_119_2) = all_154_3 & $i(all_154_2) & ( ~ % 70.11/10.12 | | | | | | | (all_154_3 = 0) | (all_154_0 = 0 & all_154_1 = 0)) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | ALPHA: (202) implies: % 70.11/10.12 | | | | | | | (203) edge(all_119_2) = all_154_3 % 70.11/10.12 | | | | | | | (204) ~ (all_154_3 = 0) | (all_154_0 = 0 & all_154_1 = 0) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | DELTA: instantiating (200) with fresh symbols all_158_0, % 70.11/10.12 | | | | | | | all_158_1, all_158_2, all_158_3 gives: % 70.11/10.12 | | | | | | | (205) on_path(all_65_5, all_20_5) = all_158_3 & % 70.11/10.12 | | | | | | | in_path(all_158_1, all_20_5) = all_158_0 & edge(all_65_5) % 70.11/10.12 | | | | | | | = all_158_2 & tail_of(all_65_5) = all_158_1 & % 70.11/10.12 | | | | | | | $i(all_158_1) & ( ~ (all_158_3 = 0) | (all_158_0 = 0 & % 70.11/10.12 | | | | | | | all_158_2 = 0 & all_107_2 = 0)) % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | ALPHA: (205) implies: % 70.11/10.12 | | | | | | | (206) $i(all_158_1) % 70.11/10.12 | | | | | | | (207) tail_of(all_65_5) = all_158_1 % 70.11/10.12 | | | | | | | % 70.11/10.12 | | | | | | | DELTA: instantiating (199) with fresh symbols all_160_0, % 70.11/10.12 | | | | | | | all_160_1, all_160_2, all_160_3 gives: % 70.11/10.13 | | | | | | | (208) on_path(all_65_5, all_20_5) = all_160_3 & % 70.11/10.13 | | | | | | | in_path(all_160_1, all_20_5) = all_160_0 & % 70.11/10.13 | | | | | | | head_of(all_65_5) = all_160_1 & edge(all_65_5) = % 70.11/10.13 | | | | | | | all_160_2 & $i(all_160_1) & ( ~ (all_160_3 = 0) | % 70.11/10.13 | | | | | | | (all_160_0 = 0 & all_160_2 = 0 & all_107_0 = 0)) % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | ALPHA: (208) implies: % 70.11/10.13 | | | | | | | (209) head_of(all_65_5) = all_160_1 % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | DELTA: instantiating (197) with fresh symbols all_168_0, all_168_1 % 70.11/10.13 | | | | | | | gives: % 70.11/10.13 | | | | | | | (210) precedes(all_119_2, all_65_5, all_20_5) = all_168_0 & % 70.11/10.13 | | | | | | | precedes(all_65_5, all_119_2, all_20_5) = all_168_1 & ( ~ % 70.11/10.13 | | | | | | | (all_168_1 = 0) | ( ~ (all_168_0 = 0) & ! [v0: $i] : ( % 70.11/10.13 | | | | | | | ~ (head_of(v0) = all_119_1) | ~ $i(v0) | ? [v1: % 70.11/10.13 | | | | | | | any] : ( ~ (v1 = all_20_4) & tail_of(v0) = v1 & % 70.11/10.13 | | | | | | | $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 70.11/10.13 | | | | | | | all_20_4) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 70.11/10.13 | | | | | | | all_119_1) & head_of(v0) = v1 & $i(v1))))) % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | ALPHA: (210) implies: % 70.11/10.13 | | | | | | | (211) precedes(all_65_5, all_119_2, all_20_5) = all_168_1 % 70.11/10.13 | | | | | | | (212) precedes(all_119_2, all_65_5, all_20_5) = all_168_0 % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | DELTA: instantiating (195) with fresh symbols all_170_0, all_170_1 % 70.11/10.13 | | | | | | | gives: % 70.11/10.13 | | | | | | | (213) precedes(all_119_2, all_65_5, all_20_5) = all_170_1 & % 70.11/10.13 | | | | | | | precedes(all_65_5, all_119_2, all_20_5) = all_170_0 & ( ~ % 70.11/10.13 | | | | | | | (all_170_1 = 0) | ( ~ (all_170_0 = 0) & ! [v0: $i] : ( % 70.11/10.13 | | | | | | | ~ (head_of(v0) = all_65_4) | ~ $i(v0) | ? [v1: % 70.11/10.13 | | | | | | | any] : ( ~ (v1 = all_119_0) & tail_of(v0) = v1 & % 70.11/10.13 | | | | | | | $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 70.11/10.13 | | | | | | | all_119_0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 70.11/10.13 | | | | | | | all_65_4) & head_of(v0) = v1 & $i(v1))))) % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | ALPHA: (213) implies: % 70.11/10.13 | | | | | | | (214) precedes(all_65_5, all_119_2, all_20_5) = all_170_0 % 70.11/10.13 | | | | | | | (215) precedes(all_119_2, all_65_5, all_20_5) = all_170_1 % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | BETA: splitting (198) gives: % 70.11/10.13 | | | | | | | % 70.11/10.13 | | | | | | | Case 1: % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | (216) all_65_4 = all_20_4 % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | REDUCE: (189), (216) imply: % 70.11/10.13 | | | | | | | | (217) $false % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | CLOSE: (217) is inconsistent. % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | Case 2: % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | (218) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (head_of(v0) % 70.11/10.13 | | | | | | | | = v1 & edge(v0) = 0 & tail_of(v0) = v2 & $i(v2) & % 70.11/10.13 | | | | | | | | $i(v1) & $i(v0) & ((v2 = all_65_4 & v1 = all_20_4) | % 70.11/10.13 | | | | | | | | (v2 = all_20_4 & v1 = all_65_4))) % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | DELTA: instantiating (218) with fresh symbols all_176_0, % 70.11/10.13 | | | | | | | | all_176_1, all_176_2 gives: % 70.11/10.13 | | | | | | | | (219) head_of(all_176_2) = all_176_1 & edge(all_176_2) = 0 & % 70.11/10.13 | | | | | | | | tail_of(all_176_2) = all_176_0 & $i(all_176_0) & % 70.11/10.13 | | | | | | | | $i(all_176_1) & $i(all_176_2) & ((all_176_0 = all_65_4 % 70.11/10.13 | | | | | | | | & all_176_1 = all_20_4) | (all_176_0 = all_20_4 & % 70.11/10.13 | | | | | | | | all_176_1 = all_65_4)) % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | ALPHA: (219) implies: % 70.11/10.13 | | | | | | | | (220) $i(all_176_2) % 70.11/10.13 | | | | | | | | (221) tail_of(all_176_2) = all_176_0 % 70.11/10.13 | | | | | | | | (222) head_of(all_176_2) = all_176_1 % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | BETA: splitting (201) gives: % 70.11/10.13 | | | | | | | | % 70.11/10.13 | | | | | | | | Case 1: % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | (223) all_113_1 = 0 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | REDUCE: (194), (223) imply: % 70.11/10.13 | | | | | | | | | (224) $false % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | CLOSE: (224) is inconsistent. % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | Case 2: % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | GROUND_INST: instantiating (26) with all_20_4, all_158_1, % 70.11/10.13 | | | | | | | | | all_65_5, simplifying with (92), (207) gives: % 70.11/10.13 | | | | | | | | | (225) all_158_1 = all_20_4 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_154_3, all_119_2, % 70.11/10.13 | | | | | | | | | simplifying with (155), (203) gives: % 70.11/10.13 | | | | | | | | | (226) all_154_3 = 0 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | GROUND_INST: instantiating (28) with all_65_4, all_160_1, % 70.11/10.13 | | | | | | | | | all_65_5, simplifying with (94), (209) gives: % 70.11/10.13 | | | | | | | | | (227) all_160_1 = all_65_4 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | GROUND_INST: instantiating (36) with all_168_1, all_170_0, % 70.11/10.13 | | | | | | | | | all_20_5, all_119_2, all_65_5, simplifying with % 70.11/10.13 | | | | | | | | | (211), (214) gives: % 70.11/10.13 | | | | | | | | | (228) all_170_0 = all_168_1 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | GROUND_INST: instantiating (36) with all_168_0, all_170_1, % 70.11/10.13 | | | | | | | | | all_20_5, all_65_5, all_119_2, simplifying with % 70.11/10.13 | | | | | | | | | (212), (215) gives: % 70.11/10.13 | | | | | | | | | (229) all_170_1 = all_168_0 % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | BETA: splitting (204) gives: % 70.11/10.13 | | | | | | | | | % 70.11/10.13 | | | | | | | | | Case 1: % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | (230) ~ (all_154_3 = 0) % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | REDUCE: (226), (230) imply: % 70.11/10.13 | | | | | | | | | | (231) $false % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | CLOSE: (231) is inconsistent. % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | Case 2: % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | GROUND_INST: instantiating (19) with all_20_4, all_20_3, % 70.11/10.13 | | | | | | | | | | all_176_2, all_176_2, all_20_5, all_176_0, % 70.11/10.13 | | | | | | | | | | all_176_1, simplifying with (41), (42), (43), % 70.11/10.13 | | | | | | | | | | (46), (220), (221), (222) gives: % 70.11/10.13 | | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : (precedes(all_176_2, % 70.11/10.13 | | | | | | | | | | all_176_2, all_20_5) = v1 & precedes(all_176_2, % 70.11/10.13 | | | | | | | | | | all_176_2, all_20_5) = v0 & ( ~ (v0 = 0) | ( ~ % 70.11/10.13 | | | | | | | | | | (v1 = 0) & ! [v2: $i] : ( ~ (head_of(v2) = % 70.11/10.13 | | | | | | | | | | all_176_1) | ~ $i(v2) | ? [v3: any] : ( % 70.11/10.13 | | | | | | | | | | ~ (v3 = all_176_0) & tail_of(v2) = v3 & % 70.11/10.13 | | | | | | | | | | $i(v3))) & ! [v2: $i] : ( ~ (tail_of(v2) % 70.11/10.13 | | | | | | | | | | = all_176_0) | ~ $i(v2) | ? [v3: any] : % 70.11/10.13 | | | | | | | | | | ( ~ (v3 = all_176_1) & head_of(v2) = v3 & % 70.11/10.13 | | | | | | | | | | $i(v3)))))) % 70.11/10.13 | | | | | | | | | | % 70.11/10.13 | | | | | | | | | | GROUND_INST: instantiating (18) with all_20_4, all_20_3, % 70.11/10.13 | | | | | | | | | | all_119_2, all_65_5, all_20_5, all_168_1, % 70.11/10.13 | | | | | | | | | | simplifying with (41), (42), (43), (46), (90), % 70.11/10.13 | | | | | | | | | | (153), (211) gives: % 70.11/10.13 | | | | | | | | | | (233) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 70.11/10.13 | | | | | | | | | | (precedes(all_119_2, all_65_5, all_20_5) = v0 & % 70.11/10.13 | | | | | | | | | | head_of(all_65_5) = v2 & tail_of(all_119_2) = v1 % 70.11/10.13 | | | | | | | | | | & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ~ (all_168_1 % 70.11/10.13 | | | | | | | | | | = 0) & ! [v3: $i] : ( ~ (head_of(v3) = v2) % 70.11/10.13 | | | | | | | | | | | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & % 70.11/10.13 | | | | | | | | | | tail_of(v3) = v4 & $i(v4))) & ! [v3: $i] % 70.11/10.13 | | | | | | | | | | : ( ~ (tail_of(v3) = v1) | ~ $i(v3) | ? % 70.11/10.13 | | | | | | | | | | [v4: $i] : ( ~ (v4 = v2) & head_of(v3) = v4 % 70.11/10.13 | | | | | | | | | | & $i(v4)))))) % 70.11/10.13 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | GROUND_INST: instantiating (18) with all_20_4, all_20_3, % 70.11/10.14 | | | | | | | | | | all_65_5, all_119_2, all_20_5, all_168_0, % 70.11/10.14 | | | | | | | | | | simplifying with (41), (42), (43), (46), (90), % 70.11/10.14 | | | | | | | | | | (153), (212) gives: % 70.11/10.14 | | | | | | | | | | (234) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 70.11/10.14 | | | | | | | | | | (precedes(all_65_5, all_119_2, all_20_5) = v0 & % 70.11/10.14 | | | | | | | | | | head_of(all_119_2) = v2 & tail_of(all_65_5) = v1 % 70.11/10.14 | | | | | | | | | | & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ~ (all_168_0 % 70.11/10.14 | | | | | | | | | | = 0) & ! [v3: $i] : ( ~ (head_of(v3) = v2) % 70.11/10.14 | | | | | | | | | | | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & % 70.11/10.14 | | | | | | | | | | tail_of(v3) = v4 & $i(v4))) & ! [v3: $i] % 70.11/10.14 | | | | | | | | | | : ( ~ (tail_of(v3) = v1) | ~ $i(v3) | ? % 70.11/10.14 | | | | | | | | | | [v4: $i] : ( ~ (v4 = v2) & head_of(v3) = v4 % 70.11/10.14 | | | | | | | | | | & $i(v4)))))) % 70.11/10.14 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_234_0, % 70.11/10.14 | | | | | | | | | | all_234_1 gives: % 70.11/10.14 | | | | | | | | | | (235) precedes(all_176_2, all_176_2, all_20_5) = % 70.11/10.14 | | | | | | | | | | all_234_0 & precedes(all_176_2, all_176_2, % 70.11/10.14 | | | | | | | | | | all_20_5) = all_234_1 & ( ~ (all_234_1 = 0) | ( ~ % 70.11/10.14 | | | | | | | | | | (all_234_0 = 0) & ! [v0: $i] : ( ~ % 70.11/10.14 | | | | | | | | | | (head_of(v0) = all_176_1) | ~ $i(v0) | ? % 70.11/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_176_0) & % 70.11/10.14 | | | | | | | | | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : % 70.11/10.14 | | | | | | | | | | ( ~ (tail_of(v0) = all_176_0) | ~ $i(v0) | ? % 70.11/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_176_1) & % 70.11/10.14 | | | | | | | | | | head_of(v0) = v1 & $i(v1))))) % 70.11/10.14 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | ALPHA: (235) implies: % 70.11/10.14 | | | | | | | | | | (236) precedes(all_176_2, all_176_2, all_20_5) = % 70.11/10.14 | | | | | | | | | | all_234_1 % 70.11/10.14 | | | | | | | | | | (237) precedes(all_176_2, all_176_2, all_20_5) = % 70.11/10.14 | | | | | | | | | | all_234_0 % 70.11/10.14 | | | | | | | | | | (238) ~ (all_234_1 = 0) | ( ~ (all_234_0 = 0) & ! [v0: % 70.11/10.14 | | | | | | | | | | $i] : ( ~ (head_of(v0) = all_176_1) | ~ $i(v0) % 70.11/10.14 | | | | | | | | | | | ? [v1: any] : ( ~ (v1 = all_176_0) & % 70.11/10.14 | | | | | | | | | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ( % 70.11/10.14 | | | | | | | | | | ~ (tail_of(v0) = all_176_0) | ~ $i(v0) | ? % 70.11/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_176_1) & head_of(v0) % 70.11/10.14 | | | | | | | | | | = v1 & $i(v1)))) % 70.11/10.14 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_240_0, % 70.11/10.14 | | | | | | | | | | all_240_1, all_240_2 gives: % 70.11/10.14 | | | | | | | | | | (239) precedes(all_65_5, all_119_2, all_20_5) = all_240_2 % 70.11/10.14 | | | | | | | | | | & head_of(all_119_2) = all_240_0 & % 70.11/10.14 | | | | | | | | | | tail_of(all_65_5) = all_240_1 & $i(all_240_0) & % 70.11/10.14 | | | | | | | | | | $i(all_240_1) & ( ~ (all_240_2 = 0) | ( ~ % 70.11/10.14 | | | | | | | | | | (all_168_0 = 0) & ! [v0: $i] : ( ~ % 70.11/10.14 | | | | | | | | | | (head_of(v0) = all_240_0) | ~ $i(v0) | ? % 70.11/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_240_1) & % 70.11/10.14 | | | | | | | | | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : % 70.11/10.14 | | | | | | | | | | ( ~ (tail_of(v0) = all_240_1) | ~ $i(v0) | ? % 70.11/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_240_0) & % 70.11/10.14 | | | | | | | | | | head_of(v0) = v1 & $i(v1))))) % 70.11/10.14 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | ALPHA: (239) implies: % 70.11/10.14 | | | | | | | | | | (240) $i(all_240_1) % 70.11/10.14 | | | | | | | | | | (241) tail_of(all_65_5) = all_240_1 % 70.11/10.14 | | | | | | | | | | % 70.11/10.14 | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_242_0, % 70.11/10.14 | | | | | | | | | | all_242_1, all_242_2 gives: % 70.44/10.14 | | | | | | | | | | (242) precedes(all_119_2, all_65_5, all_20_5) = all_242_2 % 70.44/10.14 | | | | | | | | | | & head_of(all_65_5) = all_242_0 & % 70.44/10.14 | | | | | | | | | | tail_of(all_119_2) = all_242_1 & $i(all_242_0) & % 70.44/10.14 | | | | | | | | | | $i(all_242_1) & ( ~ (all_242_2 = 0) | ( ~ % 70.44/10.14 | | | | | | | | | | (all_168_1 = 0) & ! [v0: $i] : ( ~ % 70.44/10.14 | | | | | | | | | | (head_of(v0) = all_242_0) | ~ $i(v0) | ? % 70.44/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_242_1) & % 70.44/10.14 | | | | | | | | | | tail_of(v0) = v1 & $i(v1))) & ! [v0: $i] : % 70.44/10.14 | | | | | | | | | | ( ~ (tail_of(v0) = all_242_1) | ~ $i(v0) | ? % 70.44/10.14 | | | | | | | | | | [v1: any] : ( ~ (v1 = all_242_0) & % 70.44/10.14 | | | | | | | | | | head_of(v0) = v1 & $i(v1))))) % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | ALPHA: (242) implies: % 70.44/10.14 | | | | | | | | | | (243) $i(all_242_0) % 70.44/10.14 | | | | | | | | | | (244) head_of(all_65_5) = all_242_0 % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | GROUND_INST: instantiating (26) with all_20_4, all_240_1, % 70.44/10.14 | | | | | | | | | | all_65_5, simplifying with (92), (241) gives: % 70.44/10.14 | | | | | | | | | | (245) all_240_1 = all_20_4 % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | GROUND_INST: instantiating (28) with all_65_4, all_242_0, % 70.44/10.14 | | | | | | | | | | all_65_5, simplifying with (94), (244) gives: % 70.44/10.14 | | | | | | | | | | (246) all_242_0 = all_65_4 % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | GROUND_INST: instantiating (36) with all_234_1, all_234_0, % 70.44/10.14 | | | | | | | | | | all_20_5, all_176_2, all_176_2, simplifying with % 70.44/10.14 | | | | | | | | | | (236), (237) gives: % 70.44/10.14 | | | | | | | | | | (247) all_234_0 = all_234_1 % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | BETA: splitting (238) gives: % 70.44/10.14 | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | Case 1: % 70.44/10.14 | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | (248) ~ (all_234_1 = 0) % 70.44/10.14 | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | BETA: splitting (85) gives: % 70.44/10.14 | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | Case 1: % 70.44/10.14 | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | (249) all_61_0 = 0 & all_61_1 = 0 & all_61_2 = 0 & % 70.44/10.14 | | | | | | | | | | | | sequential(all_61_4, all_61_3) = 0 & % 70.44/10.14 | | | | | | | | | | | | on_path(all_61_3, all_20_5) = 0 & % 70.44/10.14 | | | | | | | | | | | | on_path(all_61_4, all_20_5) = 0 & ! [v0: $i] : ( % 70.44/10.14 | | | | | | | | | | | | ~ (triangle(all_61_4, all_61_3, v0) = 0) | ~ % 70.44/10.14 | | | | | | | | | | | | $i(v0)) % 70.44/10.14 | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | ALPHA: (249) implies: % 70.44/10.14 | | | | | | | | | | | | (250) on_path(all_61_4, all_20_5) = 0 % 70.44/10.14 | | | | | | | | | | | | (251) on_path(all_61_3, all_20_5) = 0 % 70.44/10.14 | | | | | | | | | | | | (252) sequential(all_61_4, all_61_3) = 0 % 70.44/10.14 | | | | | | | | | | | | (253) ! [v0: $i] : ( ~ (triangle(all_61_4, all_61_3, % 70.44/10.14 | | | | | | | | | | | | v0) = 0) | ~ $i(v0)) % 70.44/10.14 | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | BETA: splitting (96) gives: % 70.44/10.14 | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | Case 1: % 70.44/10.14 | | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | | (254) ~ (all_65_3 = all_20_5) % 70.44/10.14 | | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | | BETA: splitting (95) gives: % 70.44/10.14 | | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | | Case 1: % 70.44/10.14 | | | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | | | % 70.44/10.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_20_5, all_20_4, % 70.44/10.14 | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, 0, simplifying with % 70.44/10.14 | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.14 | | | | | | | | | | | | | | (255) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 70.44/10.14 | | | | | | | | | | | | | | [v3: $i] : (precedes(all_61_4, all_61_3, all_20_5) % 70.44/10.14 | | | | | | | | | | | | | | = v0 & on_path(all_61_3, all_20_5) = v2 & % 70.44/10.14 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v1 & $i(v3) & ( ~ % 70.44/10.14 | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0 & ! [v4: $i] : ( % 70.44/10.14 | | | | | | | | | | | | | | ~ (precedes(v4, all_61_3, all_20_5) = 0) | % 70.44/10.14 | | | | | | | | | | | | | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 70.44/10.14 | | | | | | | | | | | | | | sequential(all_61_4, v4) = v5)) & ! % 70.44/10.14 | | | | | | | | | | | | | | [v4: $i] : ( ~ (sequential(all_61_4, v4) = % 70.44/10.14 | | | | | | | | | | | | | | 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 % 70.44/10.14 | | | | | | | | | | | | | | = 0) & precedes(v4, all_61_3, % 70.44/10.14 | | | | | | | | | | | | | | all_20_5) = v5))))) % 70.44/10.14 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_20_4, all_20_3, % 70.44/10.15 | | | | | | | | | | | | | | all_61_4, all_61_3, all_20_5, simplifying with % 70.44/10.15 | | | | | | | | | | | | | | (41), (42), (43), (46), (83), (84), (252) gives: % 70.44/10.15 | | | | | | | | | | | | | | (256) ? [v0: int] : ? [v1: $i] : ? [v2: int] : % 70.44/10.15 | | | | | | | | | | | | | | ($i(v1) & ((v2 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.15 | | | | | | | | | | | | | | v1) = 0) | ( ~ (v0 = 0) & % 70.44/10.15 | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.15 | | | | | | | | | | | | | | v0))) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_20_5, all_20_4, % 70.44/10.15 | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, simplifying with % 70.44/10.15 | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.15 | | | | | | | | | | | | | | (257) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 70.44/10.15 | | | | | | | | | | | | | | (precedes(all_61_4, all_61_3, all_20_5) = v2 & % 70.44/10.15 | | | | | | | | | | | | | | on_path(all_61_3, all_20_5) = v1 & % 70.44/10.15 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v0 & ( ~ (v1 = 0) % 70.44/10.15 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | DELTA: instantiating (256) with fresh symbols all_311_0, % 70.44/10.15 | | | | | | | | | | | | | | all_311_1, all_311_2 gives: % 70.44/10.15 | | | | | | | | | | | | | | (258) $i(all_311_1) & ((all_311_0 = 0 & % 70.44/10.15 | | | | | | | | | | | | | | triangle(all_61_4, all_61_3, all_311_1) = 0) | % 70.44/10.15 | | | | | | | | | | | | | | ( ~ (all_311_2 = 0) & precedes(all_61_4, % 70.44/10.15 | | | | | | | | | | | | | | all_61_3, all_20_5) = all_311_2)) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | ALPHA: (258) implies: % 70.44/10.15 | | | | | | | | | | | | | | (259) $i(all_311_1) % 70.44/10.15 | | | | | | | | | | | | | | (260) (all_311_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.15 | | | | | | | | | | | | | | all_311_1) = 0) | ( ~ (all_311_2 = 0) & % 70.44/10.15 | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.15 | | | | | | | | | | | | | | all_311_2) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | DELTA: instantiating (257) with fresh symbols all_317_0, % 70.44/10.15 | | | | | | | | | | | | | | all_317_1, all_317_2 gives: % 70.44/10.15 | | | | | | | | | | | | | | (261) precedes(all_61_4, all_61_3, all_20_5) = all_317_0 % 70.44/10.15 | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_317_1 & % 70.44/10.15 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_317_2 & ( ~ % 70.44/10.15 | | | | | | | | | | | | | | (all_317_1 = 0) | ~ (all_317_2 = 0) | all_317_0 % 70.44/10.15 | | | | | | | | | | | | | | = 0) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | ALPHA: (261) implies: % 70.44/10.15 | | | | | | | | | | | | | | (262) on_path(all_61_4, all_20_5) = all_317_2 % 70.44/10.15 | | | | | | | | | | | | | | (263) on_path(all_61_3, all_20_5) = all_317_1 % 70.44/10.15 | | | | | | | | | | | | | | (264) precedes(all_61_4, all_61_3, all_20_5) = all_317_0 % 70.44/10.15 | | | | | | | | | | | | | | (265) ~ (all_317_1 = 0) | ~ (all_317_2 = 0) | % 70.44/10.15 | | | | | | | | | | | | | | all_317_0 = 0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | DELTA: instantiating (255) with fresh symbols all_379_0, % 70.44/10.15 | | | | | | | | | | | | | | all_379_1, all_379_2, all_379_3 gives: % 70.44/10.15 | | | | | | | | | | | | | | (266) precedes(all_61_4, all_61_3, all_20_5) = all_379_3 % 70.44/10.15 | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_379_1 & % 70.44/10.15 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_379_2 & % 70.44/10.15 | | | | | | | | | | | | | | $i(all_379_0) & ( ~ (all_379_3 = 0) | (all_379_1 = % 70.44/10.15 | | | | | | | | | | | | | | 0 & all_379_2 = 0 & ! [v0: $i] : ( ~ % 70.44/10.15 | | | | | | | | | | | | | | (precedes(v0, all_61_3, all_20_5) = 0) | ~ % 70.44/10.15 | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.15 | | | | | | | | | | | | | | sequential(all_61_4, v0) = v1)) & ! [v0: % 70.44/10.15 | | | | | | | | | | | | | | $i] : ( ~ (sequential(all_61_4, v0) = 0) | % 70.44/10.15 | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.15 | | | | | | | | | | | | | | precedes(v0, all_61_3, all_20_5) = v1)))) % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | ALPHA: (266) implies: % 70.44/10.15 | | | | | | | | | | | | | | (267) on_path(all_61_4, all_20_5) = all_379_2 % 70.44/10.15 | | | | | | | | | | | | | | (268) on_path(all_61_3, all_20_5) = all_379_1 % 70.44/10.15 | | | | | | | | | | | | | | (269) precedes(all_61_4, all_61_3, all_20_5) = all_379_3 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_379_2, all_20_5, % 70.44/10.15 | | | | | | | | | | | | | | all_61_4, simplifying with (250), (267) gives: % 70.44/10.15 | | | | | | | | | | | | | | (270) all_379_2 = 0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_317_2, all_379_2, % 70.44/10.15 | | | | | | | | | | | | | | all_20_5, all_61_4, simplifying with (262), (267) % 70.44/10.15 | | | | | | | | | | | | | | gives: % 70.44/10.15 | | | | | | | | | | | | | | (271) all_379_2 = all_317_2 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_379_1, all_20_5, % 70.44/10.15 | | | | | | | | | | | | | | all_61_3, simplifying with (251), (268) gives: % 70.44/10.15 | | | | | | | | | | | | | | (272) all_379_1 = 0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_317_1, all_379_1, % 70.44/10.15 | | | | | | | | | | | | | | all_20_5, all_61_3, simplifying with (263), (268) % 70.44/10.15 | | | | | | | | | | | | | | gives: % 70.44/10.15 | | | | | | | | | | | | | | (273) all_379_1 = all_317_1 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_317_0, all_379_3, % 70.44/10.15 | | | | | | | | | | | | | | all_20_5, all_61_3, all_61_4, simplifying with % 70.44/10.15 | | | | | | | | | | | | | | (264), (269) gives: % 70.44/10.15 | | | | | | | | | | | | | | (274) all_379_3 = all_317_0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply: % 70.44/10.15 | | | | | | | | | | | | | | (275) all_317_1 = 0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply: % 70.44/10.15 | | | | | | | | | | | | | | (276) all_317_2 = 0 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | BETA: splitting (265) gives: % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | Case 1: % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | (277) ~ (all_317_1 = 0) % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | REDUCE: (275), (277) imply: % 70.44/10.15 | | | | | | | | | | | | | | | (278) $false % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | Case 2: % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | (279) ~ (all_317_2 = 0) | all_317_0 = 0 % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | Case 1: % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | (280) ~ (all_317_2 = 0) % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | REDUCE: (276), (280) imply: % 70.44/10.15 | | | | | | | | | | | | | | | | (281) $false % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | Case 2: % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | (282) all_317_0 = 0 % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | REDUCE: (264), (282) imply: % 70.44/10.15 | | | | | | | | | | | | | | | | (283) precedes(all_61_4, all_61_3, all_20_5) = 0 % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | Case 1: % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | (284) all_311_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.15 | | | | | | | | | | | | | | | | | all_311_1) = 0 % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 70.44/10.15 | | | | | | | | | | | | | | | | | (285) triangle(all_61_4, all_61_3, all_311_1) = 0 % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (253) with all_311_1, simplifying % 70.44/10.15 | | | | | | | | | | | | | | | | | with (259), (285) gives: % 70.44/10.15 | | | | | | | | | | | | | | | | | (286) $false % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | Case 2: % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | (287) ~ (all_311_2 = 0) & precedes(all_61_4, all_61_3, % 70.44/10.15 | | | | | | | | | | | | | | | | | all_20_5) = all_311_2 % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 70.44/10.15 | | | | | | | | | | | | | | | | | (288) ~ (all_311_2 = 0) % 70.44/10.15 | | | | | | | | | | | | | | | | | (289) precedes(all_61_4, all_61_3, all_20_5) = all_311_2 % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_311_2, all_20_5, % 70.44/10.15 | | | | | | | | | | | | | | | | | all_61_3, all_61_4, simplifying with (283), (289) % 70.44/10.15 | | | | | | | | | | | | | | | | | gives: % 70.44/10.15 | | | | | | | | | | | | | | | | | (290) all_311_2 = 0 % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | REDUCE: (288), (290) imply: % 70.44/10.15 | | | | | | | | | | | | | | | | | (291) $false % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 70.44/10.15 | | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | | End of split % 70.44/10.15 | | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | | End of split % 70.44/10.15 | | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | End of split % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | Case 2: % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | (292) all_65_3 = all_20_5 & all_65_4 = all_20_3 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | ALPHA: (292) implies: % 70.44/10.15 | | | | | | | | | | | | | | (293) all_65_3 = all_20_5 % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | REDUCE: (254), (293) imply: % 70.44/10.15 | | | | | | | | | | | | | | (294) $false % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | End of split % 70.44/10.15 | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | Case 2: % 70.44/10.15 | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | (295) all_65_3 = all_20_5 % 70.44/10.15 | | | | | | | | | | | | | (296) ~ (all_65_4 = all_20_3) | ( ! [v0: $i] : ( ~ % 70.44/10.15 | | | | | | | | | | | | | (path_cons(all_65_5, v0) = all_20_5) | ~ % 70.44/10.15 | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.15 | | | | | | | | | | | | | path(all_20_3, all_20_3, v0) = v1)) & ! % 70.44/10.15 | | | | | | | | | | | | | [v0: $i] : ( ~ (path(all_20_3, all_20_3, v0) = % 70.44/10.15 | | | | | | | | | | | | | 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 70.44/10.15 | | | | | | | | | | | | | all_20_5) & path_cons(all_65_5, v0) = v1 & % 70.44/10.15 | | | | | | | | | | | | | $i(v1)))) % 70.44/10.15 | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | BETA: splitting (95) gives: % 70.44/10.15 | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | Case 1: % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.15 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_20_5, all_20_4, % 70.44/10.16 | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, 0, simplifying with % 70.44/10.16 | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.16 | | | | | | | | | | | | | | (297) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 70.44/10.16 | | | | | | | | | | | | | | [v3: $i] : (precedes(all_61_4, all_61_3, all_20_5) % 70.44/10.16 | | | | | | | | | | | | | | = v0 & on_path(all_61_3, all_20_5) = v2 & % 70.44/10.16 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v1 & $i(v3) & ( ~ % 70.44/10.16 | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0 & ! [v4: $i] : ( % 70.44/10.16 | | | | | | | | | | | | | | ~ (precedes(v4, all_61_3, all_20_5) = 0) | % 70.44/10.16 | | | | | | | | | | | | | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 70.44/10.16 | | | | | | | | | | | | | | sequential(all_61_4, v4) = v5)) & ! % 70.44/10.16 | | | | | | | | | | | | | | [v4: $i] : ( ~ (sequential(all_61_4, v4) = % 70.44/10.16 | | | | | | | | | | | | | | 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 % 70.44/10.16 | | | | | | | | | | | | | | = 0) & precedes(v4, all_61_3, % 70.44/10.16 | | | | | | | | | | | | | | all_20_5) = v5))))) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_20_4, all_20_3, % 70.44/10.16 | | | | | | | | | | | | | | all_61_4, all_61_3, all_20_5, simplifying with % 70.44/10.16 | | | | | | | | | | | | | | (41), (42), (43), (46), (83), (84), (252) gives: % 70.44/10.16 | | | | | | | | | | | | | | (298) ? [v0: int] : ? [v1: $i] : ? [v2: int] : % 70.44/10.16 | | | | | | | | | | | | | | ($i(v1) & ((v2 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.16 | | | | | | | | | | | | | | v1) = 0) | ( ~ (v0 = 0) & % 70.44/10.16 | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.16 | | | | | | | | | | | | | | v0))) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_20_5, all_20_4, % 70.44/10.16 | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, simplifying with % 70.44/10.16 | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.16 | | | | | | | | | | | | | | (299) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 70.44/10.16 | | | | | | | | | | | | | | (precedes(all_61_4, all_61_3, all_20_5) = v2 & % 70.44/10.16 | | | | | | | | | | | | | | on_path(all_61_3, all_20_5) = v1 & % 70.44/10.16 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v0 & ( ~ (v1 = 0) % 70.44/10.16 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | DELTA: instantiating (298) with fresh symbols all_313_0, % 70.44/10.16 | | | | | | | | | | | | | | all_313_1, all_313_2 gives: % 70.44/10.16 | | | | | | | | | | | | | | (300) $i(all_313_1) & ((all_313_0 = 0 & % 70.44/10.16 | | | | | | | | | | | | | | triangle(all_61_4, all_61_3, all_313_1) = 0) | % 70.44/10.16 | | | | | | | | | | | | | | ( ~ (all_313_2 = 0) & precedes(all_61_4, % 70.44/10.16 | | | | | | | | | | | | | | all_61_3, all_20_5) = all_313_2)) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | ALPHA: (300) implies: % 70.44/10.16 | | | | | | | | | | | | | | (301) $i(all_313_1) % 70.44/10.16 | | | | | | | | | | | | | | (302) (all_313_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.16 | | | | | | | | | | | | | | all_313_1) = 0) | ( ~ (all_313_2 = 0) & % 70.44/10.16 | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.16 | | | | | | | | | | | | | | all_313_2) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | DELTA: instantiating (299) with fresh symbols all_319_0, % 70.44/10.16 | | | | | | | | | | | | | | all_319_1, all_319_2 gives: % 70.44/10.16 | | | | | | | | | | | | | | (303) precedes(all_61_4, all_61_3, all_20_5) = all_319_0 % 70.44/10.16 | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_319_1 & % 70.44/10.16 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_319_2 & ( ~ % 70.44/10.16 | | | | | | | | | | | | | | (all_319_1 = 0) | ~ (all_319_2 = 0) | all_319_0 % 70.44/10.16 | | | | | | | | | | | | | | = 0) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | ALPHA: (303) implies: % 70.44/10.16 | | | | | | | | | | | | | | (304) on_path(all_61_4, all_20_5) = all_319_2 % 70.44/10.16 | | | | | | | | | | | | | | (305) on_path(all_61_3, all_20_5) = all_319_1 % 70.44/10.16 | | | | | | | | | | | | | | (306) precedes(all_61_4, all_61_3, all_20_5) = all_319_0 % 70.44/10.16 | | | | | | | | | | | | | | (307) ~ (all_319_1 = 0) | ~ (all_319_2 = 0) | % 70.44/10.16 | | | | | | | | | | | | | | all_319_0 = 0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | DELTA: instantiating (297) with fresh symbols all_381_0, % 70.44/10.16 | | | | | | | | | | | | | | all_381_1, all_381_2, all_381_3 gives: % 70.44/10.16 | | | | | | | | | | | | | | (308) precedes(all_61_4, all_61_3, all_20_5) = all_381_3 % 70.44/10.16 | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_381_1 & % 70.44/10.16 | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_381_2 & % 70.44/10.16 | | | | | | | | | | | | | | $i(all_381_0) & ( ~ (all_381_3 = 0) | (all_381_1 = % 70.44/10.16 | | | | | | | | | | | | | | 0 & all_381_2 = 0 & ! [v0: $i] : ( ~ % 70.44/10.16 | | | | | | | | | | | | | | (precedes(v0, all_61_3, all_20_5) = 0) | ~ % 70.44/10.16 | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.16 | | | | | | | | | | | | | | sequential(all_61_4, v0) = v1)) & ! [v0: % 70.44/10.16 | | | | | | | | | | | | | | $i] : ( ~ (sequential(all_61_4, v0) = 0) | % 70.44/10.16 | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.16 | | | | | | | | | | | | | | precedes(v0, all_61_3, all_20_5) = v1)))) % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | ALPHA: (308) implies: % 70.44/10.16 | | | | | | | | | | | | | | (309) on_path(all_61_4, all_20_5) = all_381_2 % 70.44/10.16 | | | | | | | | | | | | | | (310) on_path(all_61_3, all_20_5) = all_381_1 % 70.44/10.16 | | | | | | | | | | | | | | (311) precedes(all_61_4, all_61_3, all_20_5) = all_381_3 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_381_2, all_20_5, % 70.44/10.16 | | | | | | | | | | | | | | all_61_4, simplifying with (250), (309) gives: % 70.44/10.16 | | | | | | | | | | | | | | (312) all_381_2 = 0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_319_2, all_381_2, % 70.44/10.16 | | | | | | | | | | | | | | all_20_5, all_61_4, simplifying with (304), (309) % 70.44/10.16 | | | | | | | | | | | | | | gives: % 70.44/10.16 | | | | | | | | | | | | | | (313) all_381_2 = all_319_2 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_381_1, all_20_5, % 70.44/10.16 | | | | | | | | | | | | | | all_61_3, simplifying with (251), (310) gives: % 70.44/10.16 | | | | | | | | | | | | | | (314) all_381_1 = 0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_319_1, all_381_1, % 70.44/10.16 | | | | | | | | | | | | | | all_20_5, all_61_3, simplifying with (305), (310) % 70.44/10.16 | | | | | | | | | | | | | | gives: % 70.44/10.16 | | | | | | | | | | | | | | (315) all_381_1 = all_319_1 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_319_0, all_381_3, % 70.44/10.16 | | | | | | | | | | | | | | all_20_5, all_61_3, all_61_4, simplifying with % 70.44/10.16 | | | | | | | | | | | | | | (306), (311) gives: % 70.44/10.16 | | | | | | | | | | | | | | (316) all_381_3 = all_319_0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | COMBINE_EQS: (314), (315) imply: % 70.44/10.16 | | | | | | | | | | | | | | (317) all_319_1 = 0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply: % 70.44/10.16 | | | | | | | | | | | | | | (318) all_319_2 = 0 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | BETA: splitting (307) gives: % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | Case 1: % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | (319) ~ (all_319_1 = 0) % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | REDUCE: (317), (319) imply: % 70.44/10.16 | | | | | | | | | | | | | | | (320) $false % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent. % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | Case 2: % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | (321) ~ (all_319_2 = 0) | all_319_0 = 0 % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | Case 1: % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | (322) ~ (all_319_2 = 0) % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | REDUCE: (318), (322) imply: % 70.44/10.16 | | | | | | | | | | | | | | | | (323) $false % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | CLOSE: (323) is inconsistent. % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | Case 2: % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | (324) all_319_0 = 0 % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | REDUCE: (306), (324) imply: % 70.44/10.16 | | | | | | | | | | | | | | | | (325) precedes(all_61_4, all_61_3, all_20_5) = 0 % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | Case 1: % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | (326) all_313_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.16 | | | | | | | | | | | | | | | | | all_313_1) = 0 % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | ALPHA: (326) implies: % 70.44/10.16 | | | | | | | | | | | | | | | | | (327) triangle(all_61_4, all_61_3, all_313_1) = 0 % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (253) with all_313_1, simplifying % 70.44/10.16 | | | | | | | | | | | | | | | | | with (301), (327) gives: % 70.44/10.16 | | | | | | | | | | | | | | | | | (328) $false % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | CLOSE: (328) is inconsistent. % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | Case 2: % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | (329) ~ (all_313_2 = 0) & precedes(all_61_4, all_61_3, % 70.44/10.16 | | | | | | | | | | | | | | | | | all_20_5) = all_313_2 % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 70.44/10.16 | | | | | | | | | | | | | | | | | (330) ~ (all_313_2 = 0) % 70.44/10.16 | | | | | | | | | | | | | | | | | (331) precedes(all_61_4, all_61_3, all_20_5) = all_313_2 % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_313_2, all_20_5, % 70.44/10.16 | | | | | | | | | | | | | | | | | all_61_3, all_61_4, simplifying with (325), (331) % 70.44/10.16 | | | | | | | | | | | | | | | | | gives: % 70.44/10.16 | | | | | | | | | | | | | | | | | (332) all_313_2 = 0 % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | REDUCE: (330), (332) imply: % 70.44/10.16 | | | | | | | | | | | | | | | | | (333) $false % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 70.44/10.16 | | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | | End of split % 70.44/10.16 | | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | End of split % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | End of split % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | Case 2: % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | (334) all_65_3 = all_20_5 & all_65_4 = all_20_3 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | ALPHA: (334) implies: % 70.44/10.16 | | | | | | | | | | | | | | (335) all_65_4 = all_20_3 % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | BETA: splitting (296) gives: % 70.44/10.16 | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | Case 1: % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | (336) ~ (all_65_4 = all_20_3) % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | REDUCE: (335), (336) imply: % 70.44/10.16 | | | | | | | | | | | | | | | (337) $false % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent. % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | Case 2: % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | % 70.44/10.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_20_5, all_20_4, % 70.44/10.16 | | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, 0, simplifying with % 70.44/10.16 | | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.17 | | | | | | | | | | | | | | | (338) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 70.44/10.17 | | | | | | | | | | | | | | | [v3: $i] : (precedes(all_61_4, all_61_3, all_20_5) % 70.44/10.17 | | | | | | | | | | | | | | | = v0 & on_path(all_61_3, all_20_5) = v2 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v1 & $i(v3) & ( ~ % 70.44/10.17 | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0 & ! [v4: $i] : ( % 70.44/10.17 | | | | | | | | | | | | | | | ~ (precedes(v4, all_61_3, all_20_5) = 0) | % 70.44/10.17 | | | | | | | | | | | | | | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 70.44/10.17 | | | | | | | | | | | | | | | sequential(all_61_4, v4) = v5)) & ! % 70.44/10.17 | | | | | | | | | | | | | | | [v4: $i] : ( ~ (sequential(all_61_4, v4) = % 70.44/10.17 | | | | | | | | | | | | | | | 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 % 70.44/10.17 | | | | | | | | | | | | | | | = 0) & precedes(v4, all_61_3, % 70.44/10.17 | | | | | | | | | | | | | | | all_20_5) = v5))))) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_20_4, all_20_3, % 70.44/10.17 | | | | | | | | | | | | | | | all_61_4, all_61_3, all_20_5, simplifying with % 70.44/10.17 | | | | | | | | | | | | | | | (41), (42), (43), (46), (83), (84), (252) gives: % 70.44/10.17 | | | | | | | | | | | | | | | (339) ? [v0: int] : ? [v1: $i] : ? [v2: int] : % 70.44/10.17 | | | | | | | | | | | | | | | ($i(v1) & ((v2 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.17 | | | | | | | | | | | | | | | v1) = 0) | ( ~ (v0 = 0) & % 70.44/10.17 | | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.17 | | | | | | | | | | | | | | | v0))) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_20_5, all_20_4, % 70.44/10.17 | | | | | | | | | | | | | | | all_20_3, all_61_4, all_61_3, simplifying with % 70.44/10.17 | | | | | | | | | | | | | | | (41), (42), (43), (61), (83), (84), (252) gives: % 70.44/10.17 | | | | | | | | | | | | | | | (340) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 70.44/10.17 | | | | | | | | | | | | | | | (precedes(all_61_4, all_61_3, all_20_5) = v2 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_61_3, all_20_5) = v1 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = v0 & ( ~ (v1 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_20_5, all_20_4, % 70.44/10.17 | | | | | | | | | | | | | | | all_20_3, all_176_2, all_176_2, all_234_1, % 70.44/10.17 | | | | | | | | | | | | | | | simplifying with (41), (42), (43), (61), (220), % 70.44/10.17 | | | | | | | | | | | | | | | (236) gives: % 70.44/10.17 | | | | | | | | | | | | | | | (341) all_234_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 70.44/10.17 | | | | | | | | | | | | | | | [v2: any] : (sequential(all_176_2, all_176_2) = v2 % 70.44/10.17 | | | | | | | | | | | | | | | & on_path(all_176_2, all_20_5) = v1 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_176_2, all_20_5) = v0 & ( ~ (v1 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | ~ (v0 = 0) | ( ~ (v2 = 0) & ! [v3: $i] : ( % 70.44/10.17 | | | | | | | | | | | | | | | ~ (precedes(v3, all_176_2, all_20_5) = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | & sequential(all_176_2, v3) = v4)) & ! % 70.44/10.17 | | | | | | | | | | | | | | | [v3: $i] : ( ~ (sequential(all_176_2, v3) = % 70.44/10.17 | | | | | | | | | | | | | | | 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 % 70.44/10.17 | | | | | | | | | | | | | | | = 0) & precedes(v3, all_176_2, % 70.44/10.17 | | | | | | | | | | | | | | | all_20_5) = v4))))) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | DELTA: instantiating (339) with fresh symbols all_324_0, % 70.44/10.17 | | | | | | | | | | | | | | | all_324_1, all_324_2 gives: % 70.44/10.17 | | | | | | | | | | | | | | | (342) $i(all_324_1) & ((all_324_0 = 0 & % 70.44/10.17 | | | | | | | | | | | | | | | triangle(all_61_4, all_61_3, all_324_1) = 0) | % 70.44/10.17 | | | | | | | | | | | | | | | ( ~ (all_324_2 = 0) & precedes(all_61_4, % 70.44/10.17 | | | | | | | | | | | | | | | all_61_3, all_20_5) = all_324_2)) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | ALPHA: (342) implies: % 70.44/10.17 | | | | | | | | | | | | | | | (343) $i(all_324_1) % 70.44/10.17 | | | | | | | | | | | | | | | (344) (all_324_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.17 | | | | | | | | | | | | | | | all_324_1) = 0) | ( ~ (all_324_2 = 0) & % 70.44/10.17 | | | | | | | | | | | | | | | precedes(all_61_4, all_61_3, all_20_5) = % 70.44/10.17 | | | | | | | | | | | | | | | all_324_2) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | DELTA: instantiating (340) with fresh symbols all_334_0, % 70.44/10.17 | | | | | | | | | | | | | | | all_334_1, all_334_2 gives: % 70.44/10.17 | | | | | | | | | | | | | | | (345) precedes(all_61_4, all_61_3, all_20_5) = all_334_0 % 70.44/10.17 | | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_334_1 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_334_2 & ( ~ % 70.44/10.17 | | | | | | | | | | | | | | | (all_334_1 = 0) | ~ (all_334_2 = 0) | all_334_0 % 70.44/10.17 | | | | | | | | | | | | | | | = 0) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | ALPHA: (345) implies: % 70.44/10.17 | | | | | | | | | | | | | | | (346) on_path(all_61_4, all_20_5) = all_334_2 % 70.44/10.17 | | | | | | | | | | | | | | | (347) on_path(all_61_3, all_20_5) = all_334_1 % 70.44/10.17 | | | | | | | | | | | | | | | (348) precedes(all_61_4, all_61_3, all_20_5) = all_334_0 % 70.44/10.17 | | | | | | | | | | | | | | | (349) ~ (all_334_1 = 0) | ~ (all_334_2 = 0) | % 70.44/10.17 | | | | | | | | | | | | | | | all_334_0 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | DELTA: instantiating (338) with fresh symbols all_369_0, % 70.44/10.17 | | | | | | | | | | | | | | | all_369_1, all_369_2, all_369_3 gives: % 70.44/10.17 | | | | | | | | | | | | | | | (350) precedes(all_61_4, all_61_3, all_20_5) = all_369_3 % 70.44/10.17 | | | | | | | | | | | | | | | & on_path(all_61_3, all_20_5) = all_369_1 & % 70.44/10.17 | | | | | | | | | | | | | | | on_path(all_61_4, all_20_5) = all_369_2 & % 70.44/10.17 | | | | | | | | | | | | | | | $i(all_369_0) & ( ~ (all_369_3 = 0) | (all_369_1 = % 70.44/10.17 | | | | | | | | | | | | | | | 0 & all_369_2 = 0 & ! [v0: $i] : ( ~ % 70.44/10.17 | | | | | | | | | | | | | | | (precedes(v0, all_61_3, all_20_5) = 0) | ~ % 70.44/10.17 | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.17 | | | | | | | | | | | | | | | sequential(all_61_4, v0) = v1)) & ! [v0: % 70.44/10.17 | | | | | | | | | | | | | | | $i] : ( ~ (sequential(all_61_4, v0) = 0) | % 70.44/10.17 | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 70.44/10.17 | | | | | | | | | | | | | | | precedes(v0, all_61_3, all_20_5) = v1)))) % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | ALPHA: (350) implies: % 70.44/10.17 | | | | | | | | | | | | | | | (351) on_path(all_61_4, all_20_5) = all_369_2 % 70.44/10.17 | | | | | | | | | | | | | | | (352) on_path(all_61_3, all_20_5) = all_369_1 % 70.44/10.17 | | | | | | | | | | | | | | | (353) precedes(all_61_4, all_61_3, all_20_5) = all_369_3 % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 70.44/10.17 | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | Case 1: % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | (354) all_234_1 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | REDUCE: (248), (354) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | (355) $false % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent. % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | Case 2: % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_369_2, all_20_5, % 70.44/10.17 | | | | | | | | | | | | | | | | all_61_4, simplifying with (250), (351) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | (356) all_369_2 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_334_2, all_369_2, % 70.44/10.17 | | | | | | | | | | | | | | | | all_20_5, all_61_4, simplifying with (346), (351) % 70.44/10.17 | | | | | | | | | | | | | | | | gives: % 70.44/10.17 | | | | | | | | | | | | | | | | (357) all_369_2 = all_334_2 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_369_1, all_20_5, % 70.44/10.17 | | | | | | | | | | | | | | | | all_61_3, simplifying with (251), (352) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | (358) all_369_1 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_334_1, all_369_1, % 70.44/10.17 | | | | | | | | | | | | | | | | all_20_5, all_61_3, simplifying with (347), (352) % 70.44/10.17 | | | | | | | | | | | | | | | | gives: % 70.44/10.17 | | | | | | | | | | | | | | | | (359) all_369_1 = all_334_1 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_334_0, all_369_3, % 70.44/10.17 | | | | | | | | | | | | | | | | all_20_5, all_61_3, all_61_4, simplifying with % 70.44/10.17 | | | | | | | | | | | | | | | | (348), (353) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | (360) all_369_3 = all_334_0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (358), (359) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | (361) all_334_1 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (357) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | (362) all_334_2 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | SIMP: (362) implies: % 70.44/10.17 | | | | | | | | | | | | | | | | (363) all_334_2 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | BETA: splitting (349) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | Case 1: % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | (364) ~ (all_334_1 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | REDUCE: (361), (364) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | | (365) $false % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent. % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | Case 2: % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | (366) ~ (all_334_2 = 0) | all_334_0 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | BETA: splitting (366) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | Case 1: % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | (367) ~ (all_334_2 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | REDUCE: (363), (367) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | | | (368) $false % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | CLOSE: (368) is inconsistent. % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | Case 2: % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | (369) all_334_0 = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | REDUCE: (348), (369) imply: % 70.44/10.17 | | | | | | | | | | | | | | | | | | (370) precedes(all_61_4, all_61_3, all_20_5) = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | Case 1: % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (371) all_324_0 = 0 & triangle(all_61_4, all_61_3, % 70.44/10.17 | | | | | | | | | | | | | | | | | | | all_324_1) = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (372) triangle(all_61_4, all_61_3, all_324_1) = 0 % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (253) with all_324_1, simplifying % 70.44/10.17 | | | | | | | | | | | | | | | | | | | with (343), (372) gives: % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (373) $false % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | CLOSE: (373) is inconsistent. % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | Case 2: % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (374) ~ (all_324_2 = 0) & precedes(all_61_4, all_61_3, % 70.44/10.17 | | | | | | | | | | | | | | | | | | | all_20_5) = all_324_2 % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.17 | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies: % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (375) ~ (all_324_2 = 0) % 70.44/10.17 | | | | | | | | | | | | | | | | | | | (376) precedes(all_61_4, all_61_3, all_20_5) = all_324_2 % 70.44/10.17 | | | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_324_2, all_20_5, % 70.44/10.18 | | | | | | | | | | | | | | | | | | | all_61_3, all_61_4, simplifying with (370), (376) % 70.44/10.18 | | | | | | | | | | | | | | | | | | | gives: % 70.44/10.18 | | | | | | | | | | | | | | | | | | | (377) all_324_2 = 0 % 70.44/10.18 | | | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | | | | REDUCE: (375), (377) imply: % 70.44/10.18 | | | | | | | | | | | | | | | | | | | (378) $false % 70.44/10.18 | | | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | | | | CLOSE: (378) is inconsistent. % 70.44/10.18 | | | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | Case 2: % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | (379) all_61_5 = all_61_6 & number_of_in(triangles, % 70.44/10.18 | | | | | | | | | | | | all_20_5) = all_61_6 & % 70.44/10.18 | | | | | | | | | | | | number_of_in(sequential_pairs, all_20_5) = % 70.44/10.18 | | | | | | | | | | | | all_61_6 & $i(all_61_6) % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | ALPHA: (379) implies: % 70.44/10.18 | | | | | | | | | | | | (380) number_of_in(sequential_pairs, all_20_5) = % 70.44/10.18 | | | | | | | | | | | | all_61_6 % 70.44/10.18 | | | | | | | | | | | | (381) number_of_in(triangles, all_20_5) = all_61_6 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_20_1, all_61_6, % 70.44/10.18 | | | | | | | | | | | | all_20_5, sequential_pairs, simplifying with % 70.44/10.18 | | | | | | | | | | | | (111), (380) gives: % 70.44/10.18 | | | | | | | | | | | | (382) all_61_6 = all_20_1 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | REDUCE: (381), (382) imply: % 70.44/10.18 | | | | | | | | | | | | (383) number_of_in(triangles, all_20_5) = all_20_1 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | GROUND_INST: instantiating (22) with triangles, all_20_5, % 70.44/10.18 | | | | | | | | | | | | all_20_1, simplifying with (23), (41), (383) % 70.44/10.18 | | | | | | | | | | | | gives: % 70.44/10.18 | | | | | | | | | | | | (384) ? [v0: $i] : (number_of_in(triangles, graph) = v0 % 70.44/10.18 | | | | | | | | | | | | & less_or_equal(all_20_1, v0) = 0 & $i(v0)) % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | DELTA: instantiating (384) with fresh symbol all_302_0 % 70.44/10.18 | | | | | | | | | | | | gives: % 70.44/10.18 | | | | | | | | | | | | (385) number_of_in(triangles, graph) = all_302_0 & % 70.44/10.18 | | | | | | | | | | | | less_or_equal(all_20_1, all_302_0) = 0 & % 70.44/10.18 | | | | | | | | | | | | $i(all_302_0) % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | ALPHA: (385) implies: % 70.44/10.18 | | | | | | | | | | | | (386) less_or_equal(all_20_1, all_302_0) = 0 % 70.44/10.18 | | | | | | | | | | | | (387) number_of_in(triangles, graph) = all_302_0 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_20_6, all_302_0, % 70.44/10.18 | | | | | | | | | | | | graph, triangles, simplifying with (47), (387) % 70.44/10.18 | | | | | | | | | | | | gives: % 70.44/10.18 | | | | | | | | | | | | (388) all_302_0 = all_20_6 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | REDUCE: (386), (388) imply: % 70.44/10.18 | | | | | | | | | | | | (389) less_or_equal(all_20_1, all_20_6) = 0 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_20_0, 0, all_20_6, % 70.44/10.18 | | | | | | | | | | | | all_20_1, simplifying with (44), (389) gives: % 70.44/10.18 | | | | | | | | | | | | (390) all_20_0 = 0 % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | REDUCE: (39), (390) imply: % 70.44/10.18 | | | | | | | | | | | | (391) $false % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | | CLOSE: (391) is inconsistent. % 70.44/10.18 | | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | Case 2: % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | (392) all_234_1 = 0 % 70.44/10.18 | | | | | | | | | | | (393) ~ (all_234_0 = 0) & ! [v0: $i] : ( ~ % 70.44/10.18 | | | | | | | | | | | (head_of(v0) = all_176_1) | ~ $i(v0) | ? [v1: % 70.44/10.18 | | | | | | | | | | | any] : ( ~ (v1 = all_176_0) & tail_of(v0) = v1 % 70.44/10.18 | | | | | | | | | | | & $i(v1))) & ! [v0: $i] : ( ~ (tail_of(v0) = % 70.44/10.18 | | | | | | | | | | | all_176_0) | ~ $i(v0) | ? [v1: any] : ( ~ % 70.44/10.18 | | | | | | | | | | | (v1 = all_176_1) & head_of(v0) = v1 & $i(v1))) % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | ALPHA: (393) implies: % 70.44/10.18 | | | | | | | | | | | (394) ~ (all_234_0 = 0) % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | COMBINE_EQS: (247), (392) imply: % 70.44/10.18 | | | | | | | | | | | (395) all_234_0 = 0 % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | REDUCE: (394), (395) imply: % 70.44/10.18 | | | | | | | | | | | (396) $false % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | | CLOSE: (396) is inconsistent. % 70.44/10.18 | | | | | | | | | | | % 70.44/10.18 | | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | | % 70.44/10.18 | | | | | | | | | End of split % 70.44/10.18 | | | | | | | | | % 70.44/10.18 | | | | | | | | End of split % 70.44/10.18 | | | | | | | | % 70.44/10.18 | | | | | | | End of split % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | Case 2: % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | | (397) all_113_1 = 0 % 70.44/10.18 | | | | | | | (398) ~ (all_113_0 = 0) & ! [v0: $i] : ( ~ (head_of(v0) = % 70.44/10.18 | | | | | | | all_65_4) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 70.44/10.18 | | | | | | | all_20_4) & tail_of(v0) = v1 & $i(v1))) & ! [v0: % 70.44/10.18 | | | | | | | $i] : ( ~ (tail_of(v0) = all_20_4) | ~ $i(v0) | ? % 70.44/10.18 | | | | | | | [v1: any] : ( ~ (v1 = all_65_4) & head_of(v0) = v1 & % 70.44/10.18 | | | | | | | $i(v1))) % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | | ALPHA: (398) implies: % 70.44/10.18 | | | | | | | (399) ~ (all_113_0 = 0) % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | | COMBINE_EQS: (168), (397) imply: % 70.44/10.18 | | | | | | | (400) all_113_0 = 0 % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | | REDUCE: (399), (400) imply: % 70.44/10.18 | | | | | | | (401) $false % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | | CLOSE: (401) is inconsistent. % 70.44/10.18 | | | | | | | % 70.44/10.18 | | | | | | End of split % 70.44/10.18 | | | | | | % 70.44/10.18 | | | | | End of split % 70.44/10.18 | | | | | % 70.44/10.18 | | | | End of split % 70.44/10.18 | | | | % 70.44/10.18 | | | End of split % 70.44/10.18 | | | % 70.44/10.18 | | End of split % 70.44/10.18 | | % 70.44/10.18 | End of split % 70.44/10.18 | % 70.44/10.18 End of proof % 70.44/10.18 % SZS output end Proof for theBenchmark % 70.44/10.18 % 70.44/10.18 9557ms %------------------------------------------------------------------------------