TSTP Solution File: GRA004+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:39:24 EDT 2023
% Result : Theorem 5.98s 2.45s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.13/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 18:07:07 EDT 2023
% 0.20/0.36 % CPUTime :
% 5.98/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.98/2.46
% 5.98/2.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.21/2.49 %$ triangle > shortest_path > precedes > path > sequential > on_path > less_or_equal > in_path > vertex > edge > path_cons > number_of_in > minus > #nlpp > tail_of > length_of > head_of > triangles > sequential_pairs > n1 > graph > empty > edges > complete > #skF_11 > #skF_6 > #skF_5 > #skF_10 > #skF_14 > #skF_13 > #skF_2 > #skF_9 > #skF_7 > #skF_4 > #skF_3 > #skF_8 > #skF_1 > #skF_12
% 6.21/2.49
% 6.21/2.49 %Foreground sorts:
% 6.21/2.49
% 6.21/2.49
% 6.21/2.49 %Background operators:
% 6.21/2.49
% 6.21/2.49
% 6.21/2.49 %Foreground operators:
% 6.21/2.49 tff(head_of, type, head_of: $i > $i).
% 6.21/2.49 tff(less_or_equal, type, less_or_equal: ($i * $i) > $o).
% 6.21/2.49 tff(triangle, type, triangle: ($i * $i * $i) > $o).
% 6.21/2.49 tff(triangles, type, triangles: $i).
% 6.21/2.49 tff('#skF_11', type, '#skF_11': $i).
% 6.21/2.49 tff('#skF_6', type, '#skF_6': ($i * $i * $i) > $i).
% 6.21/2.49 tff(number_of_in, type, number_of_in: ($i * $i) > $i).
% 6.21/2.49 tff(on_path, type, on_path: ($i * $i) > $o).
% 6.21/2.49 tff('#skF_5', type, '#skF_5': ($i * $i * $i * $i * $i) > $i).
% 6.21/2.49 tff('#skF_10', type, '#skF_10': $i).
% 6.21/2.49 tff(vertex, type, vertex: $i > $o).
% 6.21/2.49 tff(n1, type, n1: $i).
% 6.21/2.49 tff('#skF_14', type, '#skF_14': $i).
% 6.21/2.49 tff(length_of, type, length_of: $i > $i).
% 6.21/2.49 tff(sequential_pairs, type, sequential_pairs: $i).
% 6.21/2.49 tff('#skF_13', type, '#skF_13': $i).
% 6.21/2.49 tff(edge, type, edge: $i > $o).
% 6.21/2.49 tff('#skF_2', type, '#skF_2': ($i * $i * $i) > $i).
% 6.21/2.49 tff(precedes, type, precedes: ($i * $i * $i) > $o).
% 6.21/2.49 tff(graph, type, graph: $i).
% 6.21/2.49 tff('#skF_9', type, '#skF_9': $i).
% 6.21/2.49 tff('#skF_7', type, '#skF_7': ($i * $i * $i) > $i).
% 6.21/2.49 tff('#skF_4', type, '#skF_4': ($i * $i * $i * $i) > $i).
% 6.21/2.49 tff(in_path, type, in_path: ($i * $i) > $o).
% 6.21/2.49 tff(sequential, type, sequential: ($i * $i) > $o).
% 6.21/2.49 tff('#skF_3', type, '#skF_3': ($i * $i * $i) > $i).
% 6.21/2.49 tff(tail_of, type, tail_of: $i > $i).
% 6.21/2.49 tff(edges, type, edges: $i).
% 6.21/2.49 tff(complete, type, complete: $o).
% 6.21/2.49 tff(path_cons, type, path_cons: ($i * $i) > $i).
% 6.21/2.49 tff('#skF_8', type, '#skF_8': ($i * $i * $i) > $i).
% 6.21/2.49 tff(empty, type, empty: $i).
% 6.21/2.49 tff(shortest_path, type, shortest_path: ($i * $i * $i) > $o).
% 6.21/2.49 tff('#skF_1', type, '#skF_1': ($i * $i) > $i).
% 6.21/2.49 tff('#skF_12', type, '#skF_12': $i).
% 6.21/2.49 tff(path, type, path: ($i * $i * $i) > $o).
% 6.21/2.49 tff(minus, type, minus: ($i * $i) > $i).
% 6.21/2.49
% 6.21/2.51 tff(f_271, negated_conjecture, ~(![V1, V2, E1, E2, P]: ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~(?[E3]: ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & ~(head_of(E2) = tail_of(E1))) & ~(head_of(E2) = head_of(E1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', shortest_path_properties_lemma)).
% 6.21/2.51 tff(f_189, axiom, (![P, V1, V2]: (path(V1, V2, P) => (![E1, E2]: (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) ⇎ (?[E3]: (sequential(E1, E3) & precedes(E3, E2, P))))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', precedes_properties)).
% 6.21/2.51 tff(f_201, axiom, (![V1, V2, SP]: (shortest_path(V1, V2, SP) <=> ((path(V1, V2, SP) & ~(V1 = V2)) & (![P]: (path(V1, V2, P) => less_or_equal(length_of(SP), length_of(P))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', shortest_path_defn)).
% 6.21/2.51 tff(f_133, axiom, (![V1, V2, P, E]: ((path(V1, V2, P) & on_path(E, P)) => ((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', on_path_properties)).
% 6.21/2.51 tff(f_63, axiom, (![E]: (edge(E) => (vertex(head_of(E)) & vertex(tail_of(E))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', edge_ends_are_vertices)).
% 6.21/2.51 tff(f_157, axiom, (![E1, E2]: (sequential(E1, E2) <=> (((edge(E1) & edge(E2)) & ~(E1 = E2)) & (head_of(E1) = tail_of(E2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', sequential_defn)).
% 6.21/2.51 tff(f_173, axiom, (![P, V1, V2]: (path(V1, V2, P) => (![E1, E2]: (precedes(E1, E2, P) <= ((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | (?[E3]: (sequential(E1, E3) & precedes(E3, E2, P))))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', precedes_defn)).
% 6.21/2.51 tff(f_214, axiom, (![V1, V2, E1, E2, P]: ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~(?[E3]: ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & ~precedes(E2, E1, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', shortest_path_properties)).
% 6.21/2.51 tff(f_57, axiom, (![E]: (edge(E) => ~(head_of(E) = tail_of(E)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', no_loops)).
% 6.21/2.51 tff(c_142, plain, (precedes('#skF_11', '#skF_12', '#skF_13')), inference(cnfTransformation, [status(thm)], [f_271])).
% 6.21/2.51 tff(c_378, plain, (![V2_235, V1_236, E1_232, P_234, E2_233]: (on_path(E2_233, P_234) | ~precedes(E1_232, E2_233, P_234) | ~path(V1_236, V2_235, P_234))), inference(cnfTransformation, [status(thm)], [f_189])).
% 6.21/2.51 tff(c_381, plain, (![V1_236, V2_235]: (on_path('#skF_12', '#skF_13') | ~path(V1_236, V2_235, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_378])).
% 6.21/2.51 tff(c_382, plain, (![V1_236, V2_235]: (~path(V1_236, V2_235, '#skF_13'))), inference(splitLeft, [status(thm)], [c_381])).
% 6.21/2.51 tff(c_144, plain, (shortest_path('#skF_9', '#skF_10', '#skF_13')), inference(cnfTransformation, [status(thm)], [f_271])).
% 6.21/2.51 tff(c_322, plain, (![V1_207, V2_208, SP_209]: (path(V1_207, V2_208, SP_209) | ~shortest_path(V1_207, V2_208, SP_209))), inference(cnfTransformation, [status(thm)], [f_201])).
% 6.21/2.51 tff(c_326, plain, (path('#skF_9', '#skF_10', '#skF_13')), inference(resolution, [status(thm)], [c_144, c_322])).
% 6.21/2.51 tff(c_384, plain, $false, inference(negUnitSimplification, [status(thm)], [c_382, c_326])).
% 6.21/2.51 tff(c_385, plain, (on_path('#skF_12', '#skF_13')), inference(splitRight, [status(thm)], [c_381])).
% 6.21/2.51 tff(c_62, plain, (![E_29, P_28, V1_26, V2_27]: (edge(E_29) | ~on_path(E_29, P_28) | ~path(V1_26, V2_27, P_28))), inference(cnfTransformation, [status(thm)], [f_133])).
% 6.21/2.51 tff(c_388, plain, (![V1_26, V2_27]: (edge('#skF_12') | ~path(V1_26, V2_27, '#skF_13'))), inference(resolution, [status(thm)], [c_385, c_62])).
% 6.21/2.51 tff(c_390, plain, (![V1_26, V2_27]: (~path(V1_26, V2_27, '#skF_13'))), inference(splitLeft, [status(thm)], [c_388])).
% 6.21/2.51 tff(c_392, plain, $false, inference(negUnitSimplification, [status(thm)], [c_390, c_326])).
% 6.21/2.51 tff(c_393, plain, (edge('#skF_12')), inference(splitRight, [status(thm)], [c_388])).
% 6.21/2.51 tff(c_148, plain, (tail_of('#skF_11')=tail_of('#skF_14') | head_of('#skF_11')=head_of('#skF_12') | tail_of('#skF_11')=head_of('#skF_12')), inference(cnfTransformation, [status(thm)], [f_271])).
% 6.21/2.51 tff(c_156, plain, (tail_of('#skF_11')=head_of('#skF_12')), inference(splitLeft, [status(thm)], [c_148])).
% 6.21/2.51 tff(c_4, plain, (![E_2]: (vertex(tail_of(E_2)) | ~edge(E_2))), inference(cnfTransformation, [status(thm)], [f_63])).
% 6.21/2.51 tff(c_160, plain, (vertex(head_of('#skF_12')) | ~edge('#skF_11')), inference(superposition, [status(thm), theory('equality')], [c_156, c_4])).
% 6.21/2.51 tff(c_164, plain, (~edge('#skF_11')), inference(splitLeft, [status(thm)], [c_160])).
% 6.21/2.51 tff(c_176, plain, (![V1_134, V2_135, SP_136]: (path(V1_134, V2_135, SP_136) | ~shortest_path(V1_134, V2_135, SP_136))), inference(cnfTransformation, [status(thm)], [f_201])).
% 6.21/2.51 tff(c_180, plain, (path('#skF_9', '#skF_10', '#skF_13')), inference(resolution, [status(thm)], [c_144, c_176])).
% 6.21/2.51 tff(c_264, plain, (![E_171, P_172, V1_173, V2_174]: (in_path(tail_of(E_171), P_172) | ~on_path(E_171, P_172) | ~path(V1_173, V2_174, P_172))), inference(cnfTransformation, [status(thm)], [f_133])).
% 6.21/2.51 tff(c_268, plain, (![E_175]: (in_path(tail_of(E_175), '#skF_13') | ~on_path(E_175, '#skF_13'))), inference(resolution, [status(thm)], [c_180, c_264])).
% 6.21/2.51 tff(c_276, plain, (in_path(head_of('#skF_12'), '#skF_13') | ~on_path('#skF_11', '#skF_13')), inference(superposition, [status(thm), theory('equality')], [c_156, c_268])).
% 6.21/2.51 tff(c_278, plain, (~on_path('#skF_11', '#skF_13')), inference(splitLeft, [status(thm)], [c_276])).
% 6.21/2.51 tff(c_279, plain, (![E1_176, P_178, V2_179, V1_180, E2_177]: (on_path(E1_176, P_178) | ~precedes(E1_176, E2_177, P_178) | ~path(V1_180, V2_179, P_178))), inference(cnfTransformation, [status(thm)], [f_189])).
% 6.21/2.51 tff(c_281, plain, (![V1_180, V2_179]: (on_path('#skF_11', '#skF_13') | ~path(V1_180, V2_179, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_279])).
% 6.21/2.51 tff(c_284, plain, (![V1_180, V2_179]: (~path(V1_180, V2_179, '#skF_13'))), inference(negUnitSimplification, [status(thm)], [c_278, c_281])).
% 6.21/2.51 tff(c_286, plain, $false, inference(negUnitSimplification, [status(thm)], [c_284, c_180])).
% 6.21/2.51 tff(c_288, plain, (on_path('#skF_11', '#skF_13')), inference(splitRight, [status(thm)], [c_276])).
% 6.21/2.51 tff(c_290, plain, (![V1_26, V2_27]: (edge('#skF_11') | ~path(V1_26, V2_27, '#skF_13'))), inference(resolution, [status(thm)], [c_288, c_62])).
% 6.21/2.51 tff(c_293, plain, (![V1_26, V2_27]: (~path(V1_26, V2_27, '#skF_13'))), inference(negUnitSimplification, [status(thm)], [c_164, c_290])).
% 6.21/2.51 tff(c_302, plain, $false, inference(negUnitSimplification, [status(thm)], [c_293, c_180])).
% 6.21/2.51 tff(c_304, plain, (edge('#skF_11')), inference(splitRight, [status(thm)], [c_160])).
% 6.21/2.51 tff(c_70, plain, (![E1_35, E2_36]: (sequential(E1_35, E2_36) | tail_of(E2_36)!=head_of(E1_35) | E2_36=E1_35 | ~edge(E2_36) | ~edge(E1_35))), inference(cnfTransformation, [status(thm)], [f_157])).
% 6.21/2.51 tff(c_366, plain, (![V2_230, V1_231, P_229, E2_228, E1_227]: (on_path(E1_227, P_229) | ~precedes(E1_227, E2_228, P_229) | ~path(V1_231, V2_230, P_229))), inference(cnfTransformation, [status(thm)], [f_189])).
% 6.21/2.51 tff(c_369, plain, (![V1_231, V2_230]: (on_path('#skF_11', '#skF_13') | ~path(V1_231, V2_230, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_366])).
% 6.21/2.51 tff(c_370, plain, (![V1_231, V2_230]: (~path(V1_231, V2_230, '#skF_13'))), inference(splitLeft, [status(thm)], [c_369])).
% 6.21/2.51 tff(c_372, plain, $false, inference(negUnitSimplification, [status(thm)], [c_370, c_326])).
% 6.21/2.51 tff(c_373, plain, (on_path('#skF_11', '#skF_13')), inference(splitRight, [status(thm)], [c_369])).
% 6.21/2.51 tff(c_648, plain, (![E1_305, V1_304, P_306, V2_303, E2_307]: (~sequential(E1_305, E2_307) | precedes(E1_305, E2_307, P_306) | ~on_path(E2_307, P_306) | ~on_path(E1_305, P_306) | ~path(V1_304, V2_303, P_306))), inference(cnfTransformation, [status(thm)], [f_173])).
% 6.21/2.51 tff(c_658, plain, (![E1_308, E2_309]: (~sequential(E1_308, E2_309) | precedes(E1_308, E2_309, '#skF_13') | ~on_path(E2_309, '#skF_13') | ~on_path(E1_308, '#skF_13'))), inference(resolution, [status(thm)], [c_326, c_648])).
% 6.21/2.51 tff(c_453, plain, (![V2_255, E1_256, V1_253, P_252, E2_254]: (~precedes(E2_254, E1_256, P_252) | ~precedes(E1_256, E2_254, P_252) | ~shortest_path(V1_253, V2_255, P_252))), inference(cnfTransformation, [status(thm)], [f_214])).
% 6.21/2.51 tff(c_456, plain, (![V1_253, V2_255]: (~precedes('#skF_12', '#skF_11', '#skF_13') | ~shortest_path(V1_253, V2_255, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_453])).
% 6.21/2.51 tff(c_457, plain, (~precedes('#skF_12', '#skF_11', '#skF_13')), inference(splitLeft, [status(thm)], [c_456])).
% 6.21/2.51 tff(c_663, plain, (~sequential('#skF_12', '#skF_11') | ~on_path('#skF_11', '#skF_13') | ~on_path('#skF_12', '#skF_13')), inference(resolution, [status(thm)], [c_658, c_457])).
% 6.21/2.51 tff(c_673, plain, (~sequential('#skF_12', '#skF_11')), inference(demodulation, [status(thm), theory('equality')], [c_385, c_373, c_663])).
% 6.21/2.51 tff(c_679, plain, (tail_of('#skF_11')!=head_of('#skF_12') | '#skF_11'='#skF_12' | ~edge('#skF_11') | ~edge('#skF_12')), inference(resolution, [status(thm)], [c_70, c_673])).
% 6.21/2.51 tff(c_682, plain, ('#skF_11'='#skF_12'), inference(demodulation, [status(thm), theory('equality')], [c_393, c_304, c_156, c_679])).
% 6.21/2.51 tff(c_308, plain, (![E_190]: (tail_of(E_190)!=head_of(E_190) | ~edge(E_190))), inference(cnfTransformation, [status(thm)], [f_57])).
% 6.21/2.51 tff(c_311, plain, (tail_of('#skF_11')!=head_of('#skF_11')), inference(resolution, [status(thm)], [c_304, c_308])).
% 6.21/2.51 tff(c_313, plain, (head_of('#skF_11')!=head_of('#skF_12')), inference(demodulation, [status(thm), theory('equality')], [c_156, c_311])).
% 6.21/2.51 tff(c_705, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_682, c_313])).
% 6.21/2.51 tff(c_706, plain, (![V1_253, V2_255]: (~shortest_path(V1_253, V2_255, '#skF_13'))), inference(splitRight, [status(thm)], [c_456])).
% 6.21/2.51 tff(c_727, plain, $false, inference(negUnitSimplification, [status(thm)], [c_706, c_144])).
% 6.21/2.51 tff(c_729, plain, (tail_of('#skF_11')!=head_of('#skF_12')), inference(splitRight, [status(thm)], [c_148])).
% 6.21/2.51 tff(c_146, plain, (head_of('#skF_14')=head_of('#skF_12') | head_of('#skF_11')=head_of('#skF_12') | tail_of('#skF_11')=head_of('#skF_12')), inference(cnfTransformation, [status(thm)], [f_271])).
% 6.21/2.51 tff(c_731, plain, (head_of('#skF_14')=head_of('#skF_12') | head_of('#skF_11')=head_of('#skF_12')), inference(negUnitSimplification, [status(thm)], [c_729, c_146])).
% 6.21/2.51 tff(c_732, plain, (head_of('#skF_11')=head_of('#skF_12')), inference(splitLeft, [status(thm)], [c_731])).
% 6.21/2.51 tff(c_1003, plain, (![E1_465, E2_463, E3_466, V2_464, V1_462, P_461]: (head_of(E3_466)!=head_of(E2_463) | tail_of(E3_466)!=tail_of(E1_465) | ~precedes(E1_465, E2_463, P_461) | ~shortest_path(V1_462, V2_464, P_461))), inference(cnfTransformation, [status(thm)], [f_214])).
% 6.21/2.51 tff(c_1123, plain, (![E2_484, V1_483, V2_486, E1_485, P_487]: (head_of(E2_484)!=head_of('#skF_12') | tail_of(E1_485)!=tail_of('#skF_11') | ~precedes(E1_485, E2_484, P_487) | ~shortest_path(V1_483, V2_486, P_487))), inference(superposition, [status(thm), theory('equality')], [c_732, c_1003])).
% 6.21/2.51 tff(c_1126, plain, (![V1_483, V2_486]: (~shortest_path(V1_483, V2_486, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_1123])).
% 6.21/2.51 tff(c_1128, plain, $false, inference(negUnitSimplification, [status(thm)], [c_1126, c_144])).
% 6.21/2.51 tff(c_1130, plain, (head_of('#skF_11')!=head_of('#skF_12')), inference(splitRight, [status(thm)], [c_731])).
% 6.21/2.51 tff(c_728, plain, (head_of('#skF_11')=head_of('#skF_12') | tail_of('#skF_11')=tail_of('#skF_14')), inference(splitRight, [status(thm)], [c_148])).
% 6.21/2.51 tff(c_1143, plain, (tail_of('#skF_11')=tail_of('#skF_14')), inference(negUnitSimplification, [status(thm)], [c_1130, c_728])).
% 6.21/2.51 tff(c_1129, plain, (head_of('#skF_14')=head_of('#skF_12')), inference(splitRight, [status(thm)], [c_731])).
% 6.21/2.51 tff(c_1423, plain, (![V2_635, V1_633, E2_634, P_632, E1_636, E3_637]: (head_of(E3_637)!=head_of(E2_634) | tail_of(E3_637)!=tail_of(E1_636) | ~precedes(E1_636, E2_634, P_632) | ~shortest_path(V1_633, V2_635, P_632))), inference(cnfTransformation, [status(thm)], [f_214])).
% 6.21/2.51 tff(c_1526, plain, (![V2_649, E2_650, E1_651, V1_647, P_648]: (head_of(E2_650)!=head_of('#skF_12') | tail_of(E1_651)!=tail_of('#skF_14') | ~precedes(E1_651, E2_650, P_648) | ~shortest_path(V1_647, V2_649, P_648))), inference(superposition, [status(thm), theory('equality')], [c_1129, c_1423])).
% 6.21/2.51 tff(c_1528, plain, (![V1_647, V2_649]: (tail_of('#skF_11')!=tail_of('#skF_14') | ~shortest_path(V1_647, V2_649, '#skF_13'))), inference(resolution, [status(thm)], [c_142, c_1526])).
% 6.21/2.51 tff(c_1531, plain, (![V1_647, V2_649]: (~shortest_path(V1_647, V2_649, '#skF_13'))), inference(demodulation, [status(thm), theory('equality')], [c_1143, c_1528])).
% 6.21/2.51 tff(c_1533, plain, $false, inference(negUnitSimplification, [status(thm)], [c_1531, c_144])).
% 6.21/2.51 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.21/2.51
% 6.21/2.51 Inference rules
% 6.21/2.51 ----------------------
% 6.21/2.51 #Ref : 4
% 6.21/2.51 #Sup : 296
% 6.21/2.51 #Fact : 0
% 6.21/2.51 #Define : 0
% 6.21/2.51 #Split : 46
% 6.21/2.51 #Chain : 0
% 6.21/2.51 #Close : 0
% 6.21/2.51
% 6.21/2.51 Ordering : KBO
% 6.21/2.51
% 6.21/2.51 Simplification rules
% 6.21/2.51 ----------------------
% 6.21/2.51 #Subsume : 27
% 6.21/2.51 #Demod : 80
% 6.21/2.51 #Tautology : 96
% 6.21/2.51 #SimpNegUnit : 37
% 6.21/2.51 #BackRed : 50
% 6.21/2.51
% 6.21/2.51 #Partial instantiations: 0
% 6.21/2.51 #Strategies tried : 1
% 6.21/2.51
% 6.21/2.51 Timing (in seconds)
% 6.21/2.51 ----------------------
% 6.21/2.51 Preprocessing : 0.66
% 6.21/2.51 Parsing : 0.30
% 6.21/2.51 CNF conversion : 0.05
% 6.21/2.51 Main loop : 0.75
% 6.21/2.51 Inferencing : 0.28
% 6.21/2.51 Reduction : 0.21
% 6.21/2.51 Demodulation : 0.14
% 6.21/2.51 BG Simplification : 0.05
% 6.21/2.51 Subsumption : 0.14
% 6.21/2.51 Abstraction : 0.03
% 6.21/2.51 MUC search : 0.00
% 6.21/2.51 Cooper : 0.00
% 6.21/2.51 Total : 1.48
% 6.21/2.51 Index Insertion : 0.00
% 6.21/2.51 Index Deletion : 0.00
% 6.21/2.51 Index Matching : 0.00
% 6.21/2.51 BG Taut test : 0.00
%------------------------------------------------------------------------------