%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 9.12s 2.10s % Output : Proof 11.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Aug 27 03:56:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.63 ________ _____ % 0.19/0.63 ___ __ \_________(_)________________________________ % 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.63 % 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.63 (2023-06-19) % 0.19/0.63 % 0.19/0.63 (c) Philipp Rümmer, 2009-2023 % 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.63 Amanda Stjerna. % 0.19/0.63 Free software under BSD-3-Clause. % 0.19/0.63 % 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.63 % 0.19/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.22/1.24 Prover 4: Preprocessing ... % 3.22/1.24 Prover 1: Preprocessing ... % 3.22/1.28 Prover 3: Preprocessing ... % 3.22/1.28 Prover 2: Preprocessing ... % 3.22/1.28 Prover 5: Preprocessing ... % 3.22/1.28 Prover 6: Preprocessing ... % 3.89/1.29 Prover 0: Preprocessing ... % 7.79/1.82 Prover 3: Constructing countermodel ... % 7.79/1.84 Prover 6: Proving ... % 7.79/1.86 Prover 1: Constructing countermodel ... % 7.79/1.86 Prover 5: Proving ... % 7.79/1.89 Prover 2: Proving ... % 9.12/2.01 Prover 0: Proving ... % 9.12/2.02 Prover 4: Constructing countermodel ... % 9.12/2.10 Prover 6: proved (1449ms) % 9.12/2.10 % 9.12/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.12/2.10 % 9.39/2.10 Prover 3: stopped % 9.39/2.11 Prover 2: stopped % 9.39/2.11 Prover 5: stopped % 9.39/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.39/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.39/2.11 Prover 0: stopped % 9.39/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.39/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.39/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.94/2.17 Prover 1: Found proof (size 41) % 9.94/2.17 Prover 1: proved (1525ms) % 9.94/2.17 Prover 4: stopped % 9.94/2.18 Prover 11: Preprocessing ... % 9.94/2.18 Prover 7: Preprocessing ... % 9.94/2.19 Prover 10: Preprocessing ... % 9.94/2.19 Prover 8: Preprocessing ... % 9.94/2.21 Prover 13: Preprocessing ... % 10.71/2.22 Prover 7: stopped % 10.71/2.22 Prover 10: stopped % 10.71/2.24 Prover 11: stopped % 10.71/2.25 Prover 13: stopped % 11.18/2.31 Prover 8: Warning: ignoring some quantifiers % 11.18/2.32 Prover 8: Constructing countermodel ... % 11.18/2.32 Prover 8: stopped % 11.18/2.32 % 11.18/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.18/2.32 % 11.18/2.33 % SZS output start Proof for theBenchmark % 11.18/2.33 Assumptions after simplification: % 11.18/2.33 --------------------------------- % 11.18/2.33 % 11.18/2.33 (graph_has_them_all) % 11.18/2.36 $i(graph) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 11.18/2.36 int] : (v4 = 0 | ~ (number_of_in(v0, v1) = v2) | ~ (number_of_in(v0, % 11.18/2.36 graph) = v3) | ~ (less_or_equal(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0)) % 11.18/2.36 % 11.18/2.36 (length_defn) % 11.18/2.36 $i(edges) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = % 11.18/2.36 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 11.18/2.36 (number_of_in(edges, v2) = v3 & length_of(v2) = v3 & $i(v3))) % 11.18/2.36 % 11.18/2.36 (maximal_path_length) % 11.18/2.36 $i(graph) & $i(triangles) & $i(n1) & ? [v0: $i] : (number_of_in(triangles, % 11.18/2.36 graph) = v0 & $i(v0) & complete & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 11.18/2.36 : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & minus(v4, n1) = % 11.18/2.36 v5 & shortest_path(v2, v3, v1) = 0 & length_of(v1) = v4 & % 11.18/2.36 less_or_equal(v5, v0) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 11.18/2.36 % 11.18/2.36 (path_length_sequential_pairs) % 11.18/2.37 $i(n1) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.18/2.37 (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 11.18/2.37 ? [v4: $i] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 11.18/2.37 length_of(v2) = v4 & $i(v4) & $i(v3))) % 11.18/2.37 % 11.18/2.37 (shortest_path_defn) % 11.18/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | % 11.18/2.37 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.18/2.37 [v4: any] : ? [v5: $i] : (length_of(v2) = v5 & path(v0, v1, v2) = v4 & % 11.18/2.37 $i(v5) & ( ~ (v4 = 0) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 % 11.18/2.37 = 0) & length_of(v6) = v7 & less_or_equal(v5, v7) = v8 & path(v0, % 11.18/2.37 v1, v6) = 0 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! % 11.18/2.37 [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.18/2.37 $i(v0) | ( ~ (v1 = v0) & ? [v3: $i] : (length_of(v2) = v3 & path(v0, v1, % 11.18/2.37 v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 % 11.18/2.37 | ~ (length_of(v4) = v5) | ~ (less_or_equal(v3, v5) = v6) | ~ % 11.18/2.37 $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & path(v0, v1, v4) = v7))))) % 11.18/2.37 % 11.18/2.37 (triangles_and_sequential_pairs) % 11.18/2.37 $i(triangles) & $i(sequential_pairs) & ( ~ complete | ! [v0: $i] : ! [v1: % 11.18/2.37 $i] : ! [v2: $i] : ( ~ (shortest_path(v1, v2, v0) = 0) | ~ $i(v2) | ~ % 11.18/2.37 $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 & % 11.18/2.37 number_of_in(sequential_pairs, v0) = v3 & $i(v3)))) % 11.18/2.37 % 11.18/2.37 (function-axioms) % 11.61/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.61/2.38 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~ % 11.61/2.38 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 11.61/2.38 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & ! % 11.61/2.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.61/2.38 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~ % 11.61/2.38 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 11.61/2.38 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 11.61/2.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 11.61/2.38 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.61/2.38 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = % 11.61/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.61/2.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ % 11.61/2.38 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.61/2.38 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0: % 11.61/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.61/2.38 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0: % 11.61/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.61/2.38 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0: % 11.61/2.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3, % 11.61/2.38 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 11.61/2.38 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) & % 11.61/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 11.61/2.38 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1: % 11.61/2.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) = % 11.61/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.61/2.38 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : ! % 11.61/2.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) = % 11.61/2.38 v0)) % 11.61/2.38 % 11.61/2.38 Further assumptions not needed in the proof: % 11.61/2.38 -------------------------------------------- % 11.61/2.38 complete_properties, edge_ends_are_vertices, in_path_properties, no_loops, % 11.61/2.38 on_path_properties, path_defn, path_properties, precedes_defn, % 11.61/2.38 precedes_properties, sequential_defn, sequential_pairs_and_triangles, % 11.61/2.38 shortest_path_properties, triangle_defn % 11.61/2.38 % 11.61/2.38 Those formulas are unsatisfiable: % 11.61/2.38 --------------------------------- % 11.61/2.38 % 11.61/2.38 Begin of proof % 11.61/2.38 | % 11.61/2.38 | ALPHA: (shortest_path_defn) implies: % 11.61/2.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1, % 11.61/2.39 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? % 11.61/2.39 | [v3: $i] : (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & ! % 11.61/2.39 | [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 11.61/2.39 | (length_of(v4) = v5) | ~ (less_or_equal(v3, v5) = v6) | ~ % 11.61/2.39 | $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & path(v0, v1, v4) = % 11.61/2.39 | v7))))) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (length_defn) implies: % 11.61/2.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 11.61/2.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(edges, % 11.61/2.39 | v2) = v3 & length_of(v2) = v3 & $i(v3))) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (path_length_sequential_pairs) implies: % 11.61/2.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) | % 11.61/2.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.61/2.39 | (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 & % 11.61/2.39 | length_of(v2) = v4 & $i(v4) & $i(v3))) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (graph_has_them_all) implies: % 11.61/2.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.61/2.39 | (v4 = 0 | ~ (number_of_in(v0, v1) = v2) | ~ (number_of_in(v0, graph) % 11.61/2.39 | = v3) | ~ (less_or_equal(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0)) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (triangles_and_sequential_pairs) implies: % 11.61/2.39 | (5) ~ complete | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.61/2.39 | (shortest_path(v1, v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.61/2.39 | ? [v3: $i] : (number_of_in(triangles, v0) = v3 & % 11.61/2.39 | number_of_in(sequential_pairs, v0) = v3 & $i(v3))) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (maximal_path_length) implies: % 11.61/2.39 | (6) $i(triangles) % 11.61/2.39 | (7) ? [v0: $i] : (number_of_in(triangles, graph) = v0 & $i(v0) & complete % 11.61/2.39 | & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 11.61/2.39 | : ? [v6: int] : ( ~ (v6 = 0) & minus(v4, n1) = v5 & % 11.61/2.39 | shortest_path(v2, v3, v1) = 0 & length_of(v1) = v4 & % 11.61/2.39 | less_or_equal(v5, v0) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 11.61/2.39 | $i(v1))) % 11.61/2.39 | % 11.61/2.39 | ALPHA: (function-axioms) implies: % 11.61/2.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) % 11.61/2.39 | = v1) | ~ (length_of(v2) = v0)) % 11.61/2.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.61/2.39 | (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0)) % 11.61/2.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.61/2.39 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 11.61/2.39 | % 11.61/2.40 | DELTA: instantiating (7) with fresh symbol all_20_0 gives: % 11.61/2.40 | (11) number_of_in(triangles, graph) = all_20_0 & $i(all_20_0) & complete & % 11.61/2.40 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 11.61/2.40 | ? [v5: int] : ( ~ (v5 = 0) & minus(v3, n1) = v4 & shortest_path(v1, % 11.61/2.40 | v2, v0) = 0 & length_of(v0) = v3 & less_or_equal(v4, all_20_0) = % 11.61/2.40 | v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.61/2.40 | % 11.61/2.40 | ALPHA: (11) implies: % 11.61/2.40 | (12) complete % 11.61/2.40 | (13) number_of_in(triangles, graph) = all_20_0 % 11.61/2.40 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 11.61/2.40 | ? [v5: int] : ( ~ (v5 = 0) & minus(v3, n1) = v4 & shortest_path(v1, % 11.61/2.40 | v2, v0) = 0 & length_of(v0) = v3 & less_or_equal(v4, all_20_0) = % 11.61/2.40 | v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.61/2.40 | % 11.61/2.40 | DELTA: instantiating (14) with fresh symbols all_22_0, all_22_1, all_22_2, % 11.61/2.40 | all_22_3, all_22_4, all_22_5 gives: % 11.71/2.40 | (15) ~ (all_22_0 = 0) & minus(all_22_2, n1) = all_22_1 & % 11.71/2.40 | shortest_path(all_22_4, all_22_3, all_22_5) = 0 & length_of(all_22_5) % 11.71/2.40 | = all_22_2 & less_or_equal(all_22_1, all_20_0) = all_22_0 & % 11.71/2.40 | $i(all_22_1) & $i(all_22_2) & $i(all_22_3) & $i(all_22_4) & % 11.71/2.40 | $i(all_22_5) % 11.71/2.40 | % 11.71/2.40 | ALPHA: (15) implies: % 11.71/2.40 | (16) ~ (all_22_0 = 0) % 11.71/2.40 | (17) $i(all_22_5) % 11.71/2.40 | (18) $i(all_22_4) % 11.71/2.40 | (19) $i(all_22_3) % 11.71/2.40 | (20) less_or_equal(all_22_1, all_20_0) = all_22_0 % 11.71/2.40 | (21) length_of(all_22_5) = all_22_2 % 11.71/2.40 | (22) shortest_path(all_22_4, all_22_3, all_22_5) = 0 % 11.71/2.40 | (23) minus(all_22_2, n1) = all_22_1 % 11.71/2.40 | % 11.71/2.40 | BETA: splitting (5) gives: % 11.71/2.40 | % 11.71/2.40 | Case 1: % 11.71/2.40 | | % 11.71/2.40 | | (24) ~ complete % 11.71/2.40 | | % 11.71/2.40 | | PRED_UNIFY: (12), (24) imply: % 11.71/2.40 | | (25) $false % 11.71/2.40 | | % 11.71/2.40 | | CLOSE: (25) is inconsistent. % 11.71/2.40 | | % 11.71/2.40 | Case 2: % 11.71/2.40 | | % 11.71/2.40 | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v1, v2, % 11.71/2.40 | | v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 11.71/2.40 | | (number_of_in(triangles, v0) = v3 & number_of_in(sequential_pairs, % 11.71/2.40 | | v0) = v3 & $i(v3))) % 11.71/2.40 | | % 11.71/2.41 | | GROUND_INST: instantiating (26) with all_22_5, all_22_4, all_22_3, % 11.71/2.41 | | simplifying with (17), (18), (19), (22) gives: % 11.71/2.41 | | (27) ? [v0: $i] : (number_of_in(triangles, all_22_5) = v0 & % 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = v0 & $i(v0)) % 11.71/2.41 | | % 11.71/2.41 | | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_5, % 11.71/2.41 | | simplifying with (17), (18), (19), (22) gives: % 11.71/2.41 | | (28) ~ (all_22_3 = all_22_4) & ? [v0: $i] : (length_of(all_22_5) = v0 & % 11.71/2.41 | | path(all_22_4, all_22_3, all_22_5) = 0 & $i(v0) & ! [v1: $i] : ! % 11.71/2.41 | | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (length_of(v1) = v2) | ~ % 11.71/2.41 | | (less_or_equal(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ % 11.71/2.41 | | (v4 = 0) & path(all_22_4, all_22_3, v1) = v4))) % 11.71/2.41 | | % 11.71/2.41 | | ALPHA: (28) implies: % 11.71/2.41 | | (29) ? [v0: $i] : (length_of(all_22_5) = v0 & path(all_22_4, all_22_3, % 11.71/2.41 | | all_22_5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.71/2.41 | | int] : (v3 = 0 | ~ (length_of(v1) = v2) | ~ (less_or_equal(v0, % 11.71/2.41 | | v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 11.71/2.41 | | path(all_22_4, all_22_3, v1) = v4))) % 11.71/2.41 | | % 11.71/2.41 | | DELTA: instantiating (27) with fresh symbol all_39_0 gives: % 11.71/2.41 | | (30) number_of_in(triangles, all_22_5) = all_39_0 & % 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = all_39_0 & $i(all_39_0) % 11.71/2.41 | | % 11.71/2.41 | | ALPHA: (30) implies: % 11.71/2.41 | | (31) number_of_in(sequential_pairs, all_22_5) = all_39_0 % 11.71/2.41 | | (32) number_of_in(triangles, all_22_5) = all_39_0 % 11.71/2.41 | | % 11.71/2.41 | | DELTA: instantiating (29) with fresh symbol all_41_0 gives: % 11.71/2.41 | | (33) length_of(all_22_5) = all_41_0 & path(all_22_4, all_22_3, all_22_5) % 11.71/2.41 | | = 0 & $i(all_41_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 % 11.71/2.41 | | = 0 | ~ (length_of(v0) = v1) | ~ (less_or_equal(all_41_0, v1) = % 11.71/2.41 | | v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & path(all_22_4, % 11.71/2.41 | | all_22_3, v0) = v3)) % 11.71/2.41 | | % 11.71/2.41 | | ALPHA: (33) implies: % 11.71/2.41 | | (34) path(all_22_4, all_22_3, all_22_5) = 0 % 11.71/2.41 | | (35) length_of(all_22_5) = all_41_0 % 11.71/2.41 | | % 11.71/2.41 | | GROUND_INST: instantiating (8) with all_22_2, all_41_0, all_22_5, % 11.71/2.41 | | simplifying with (21), (35) gives: % 11.71/2.41 | | (36) all_41_0 = all_22_2 % 11.71/2.41 | | % 11.71/2.41 | | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_5, % 11.71/2.41 | | simplifying with (17), (18), (19), (34) gives: % 11.71/2.41 | | (37) ? [v0: $i] : ? [v1: $i] : (minus(v1, n1) = v0 & % 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = v0 & % 11.71/2.41 | | length_of(all_22_5) = v1 & $i(v1) & $i(v0)) % 11.71/2.41 | | % 11.71/2.41 | | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_5, % 11.71/2.41 | | simplifying with (17), (18), (19), (34) gives: % 11.71/2.41 | | (38) ? [v0: $i] : (number_of_in(edges, all_22_5) = v0 & % 11.71/2.41 | | length_of(all_22_5) = v0 & $i(v0)) % 11.71/2.41 | | % 11.71/2.41 | | DELTA: instantiating (38) with fresh symbol all_56_0 gives: % 11.71/2.41 | | (39) number_of_in(edges, all_22_5) = all_56_0 & length_of(all_22_5) = % 11.71/2.41 | | all_56_0 & $i(all_56_0) % 11.79/2.41 | | % 11.79/2.41 | | ALPHA: (39) implies: % 11.79/2.41 | | (40) length_of(all_22_5) = all_56_0 % 11.79/2.41 | | % 11.79/2.41 | | DELTA: instantiating (37) with fresh symbols all_58_0, all_58_1 gives: % 11.79/2.42 | | (41) minus(all_58_0, n1) = all_58_1 & number_of_in(sequential_pairs, % 11.79/2.42 | | all_22_5) = all_58_1 & length_of(all_22_5) = all_58_0 & % 11.79/2.42 | | $i(all_58_0) & $i(all_58_1) % 11.79/2.42 | | % 11.79/2.42 | | ALPHA: (41) implies: % 11.79/2.42 | | (42) length_of(all_22_5) = all_58_0 % 11.79/2.42 | | (43) number_of_in(sequential_pairs, all_22_5) = all_58_1 % 11.79/2.42 | | (44) minus(all_58_0, n1) = all_58_1 % 11.79/2.42 | | % 11.79/2.42 | | GROUND_INST: instantiating (8) with all_22_2, all_58_0, all_22_5, % 11.79/2.42 | | simplifying with (21), (42) gives: % 11.79/2.42 | | (45) all_58_0 = all_22_2 % 11.79/2.42 | | % 11.79/2.42 | | GROUND_INST: instantiating (8) with all_56_0, all_58_0, all_22_5, % 11.79/2.42 | | simplifying with (40), (42) gives: % 11.79/2.42 | | (46) all_58_0 = all_56_0 % 11.79/2.42 | | % 11.79/2.42 | | GROUND_INST: instantiating (9) with all_39_0, all_58_1, all_22_5, % 11.79/2.42 | | sequential_pairs, simplifying with (31), (43) gives: % 11.79/2.42 | | (47) all_58_1 = all_39_0 % 11.79/2.42 | | % 11.79/2.42 | | COMBINE_EQS: (45), (46) imply: % 11.79/2.42 | | (48) all_56_0 = all_22_2 % 11.79/2.42 | | % 11.79/2.42 | | REDUCE: (44), (45), (47) imply: % 11.79/2.42 | | (49) minus(all_22_2, n1) = all_39_0 % 11.79/2.42 | | % 11.79/2.42 | | GROUND_INST: instantiating (10) with all_22_1, all_39_0, n1, all_22_2, % 11.79/2.42 | | simplifying with (23), (49) gives: % 11.79/2.42 | | (50) all_39_0 = all_22_1 % 11.79/2.42 | | % 11.79/2.42 | | REDUCE: (32), (50) imply: % 11.79/2.42 | | (51) number_of_in(triangles, all_22_5) = all_22_1 % 11.79/2.42 | | % 11.79/2.42 | | GROUND_INST: instantiating (4) with triangles, all_22_5, all_22_1, all_20_0, % 11.79/2.42 | | all_22_0, simplifying with (6), (13), (17), (20), (51) gives: % 11.79/2.42 | | (52) all_22_0 = 0 % 11.79/2.42 | | % 11.79/2.42 | | REDUCE: (16), (52) imply: % 11.79/2.42 | | (53) $false % 11.79/2.42 | | % 11.79/2.42 | | CLOSE: (53) is inconsistent. % 11.79/2.42 | | % 11.79/2.42 | End of split % 11.79/2.42 | % 11.79/2.42 End of proof % 11.79/2.42 % SZS output end Proof for theBenchmark % 11.79/2.42 % 11.79/2.42 1792ms %------------------------------------------------------------------------------