TSTP Solution File: GRA003+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRA003+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n013.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 4.38s 2.17s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.15/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 18:02:32 EDT 2023
% 0.15/0.37 % CPUTime :
% 4.38/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/2.17
% 4.38/2.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/2.19 %$ 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_13 > #skF_2 > #skF_9 > #skF_7 > #skF_4 > #skF_3 > #skF_8 > #skF_1 > #skF_12
% 4.38/2.19
% 4.38/2.19 %Foreground sorts:
% 4.38/2.19
% 4.38/2.19
% 4.38/2.19 %Background operators:
% 4.38/2.19
% 4.38/2.19
% 4.38/2.19 %Foreground operators:
% 4.38/2.19 tff(head_of, type, head_of: $i > $i).
% 4.38/2.19 tff(less_or_equal, type, less_or_equal: ($i * $i) > $o).
% 4.38/2.19 tff(triangle, type, triangle: ($i * $i * $i) > $o).
% 4.38/2.19 tff(triangles, type, triangles: $i).
% 4.38/2.19 tff('#skF_11', type, '#skF_11': $i).
% 4.38/2.19 tff('#skF_6', type, '#skF_6': ($i * $i * $i) > $i).
% 4.38/2.19 tff(number_of_in, type, number_of_in: ($i * $i) > $i).
% 4.38/2.19 tff(on_path, type, on_path: ($i * $i) > $o).
% 4.38/2.19 tff('#skF_5', type, '#skF_5': ($i * $i * $i * $i * $i) > $i).
% 4.38/2.19 tff('#skF_10', type, '#skF_10': $i).
% 4.38/2.19 tff(vertex, type, vertex: $i > $o).
% 4.38/2.19 tff(n1, type, n1: $i).
% 4.38/2.19 tff(length_of, type, length_of: $i > $i).
% 4.38/2.19 tff(sequential_pairs, type, sequential_pairs: $i).
% 4.38/2.19 tff('#skF_13', type, '#skF_13': $i).
% 4.38/2.19 tff(edge, type, edge: $i > $o).
% 4.38/2.19 tff('#skF_2', type, '#skF_2': ($i * $i * $i) > $i).
% 4.38/2.19 tff(precedes, type, precedes: ($i * $i * $i) > $o).
% 4.38/2.19 tff(graph, type, graph: $i).
% 4.38/2.19 tff('#skF_9', type, '#skF_9': $i).
% 4.38/2.19 tff('#skF_7', type, '#skF_7': ($i * $i * $i) > $i).
% 4.38/2.19 tff('#skF_4', type, '#skF_4': ($i * $i * $i * $i) > $i).
% 4.38/2.19 tff(in_path, type, in_path: ($i * $i) > $o).
% 4.38/2.19 tff(sequential, type, sequential: ($i * $i) > $o).
% 4.38/2.19 tff('#skF_3', type, '#skF_3': ($i * $i * $i) > $i).
% 4.38/2.19 tff(tail_of, type, tail_of: $i > $i).
% 4.38/2.19 tff(edges, type, edges: $i).
% 4.38/2.19 tff(complete, type, complete: $o).
% 4.38/2.19 tff(path_cons, type, path_cons: ($i * $i) > $i).
% 4.38/2.19 tff('#skF_8', type, '#skF_8': ($i * $i * $i) > $i).
% 4.38/2.19 tff(empty, type, empty: $i).
% 4.38/2.19 tff(shortest_path, type, shortest_path: ($i * $i * $i) > $o).
% 4.38/2.19 tff('#skF_1', type, '#skF_1': ($i * $i) > $i).
% 4.38/2.19 tff('#skF_12', type, '#skF_12': $i).
% 4.38/2.19 tff(path, type, path: ($i * $i * $i) > $o).
% 4.38/2.19 tff(minus, type, minus: ($i * $i) > $i).
% 4.38/2.19
% 4.38/2.21 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/sandbox/benchmark/Axioms/GRA001+0.ax', shortest_path_defn)).
% 4.38/2.21 tff(f_275, negated_conjecture, ~(![V1, V2, E1, E2, P]: ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((((((vertex(V1) & vertex(V2)) & ~(V1 = V2)) & edge(E1)) & edge(E2)) & ~(E1 = E2)) & path(V1, V2, P)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vertices_and_edges)).
% 4.38/2.21 tff(f_123, axiom, (![V1, V2, P]: (path(V1, V2, P) => ((vertex(V1) & vertex(V2)) & (?[E]: ((edge(E) & (V1 = tail_of(E))) & (((V2 = head_of(E)) & (P = path_cons(E, empty))) ⇎ (?[TP]: (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', path_properties)).
% 4.38/2.21 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/sandbox/benchmark/Axioms/GRA001+0.ax', precedes_properties)).
% 4.38/2.21 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/sandbox/benchmark/Axioms/GRA001+0.ax', on_path_properties)).
% 4.38/2.21 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/sandbox/benchmark/Axioms/GRA001+0.ax', shortest_path_properties)).
% 4.38/2.21 tff(c_102, plain, (![V2_63, SP_64]: (~shortest_path(V2_63, V2_63, SP_64))), inference(cnfTransformation, [status(thm)], [f_201])).
% 4.38/2.21 tff(c_142, plain, (~path('#skF_9', '#skF_10', '#skF_13') | '#skF_11'='#skF_12' | ~edge('#skF_12') | ~edge('#skF_11') | '#skF_10'='#skF_9' | ~vertex('#skF_10') | ~vertex('#skF_9')), inference(cnfTransformation, [status(thm)], [f_275])).
% 4.38/2.21 tff(c_154, plain, (~vertex('#skF_9')), inference(splitLeft, [status(thm)], [c_142])).
% 4.38/2.21 tff(c_146, plain, (shortest_path('#skF_9', '#skF_10', '#skF_13')), inference(cnfTransformation, [status(thm)], [f_275])).
% 4.38/2.21 tff(c_165, plain, (![V1_133, V2_134, SP_135]: (path(V1_133, V2_134, SP_135) | ~shortest_path(V1_133, V2_134, SP_135))), inference(cnfTransformation, [status(thm)], [f_201])).
% 4.38/2.21 tff(c_169, plain, (path('#skF_9', '#skF_10', '#skF_13')), inference(resolution, [status(thm)], [c_146, c_165])).
% 4.38/2.21 tff(c_38, plain, (![V1_15, V2_16, P_17]: (vertex(V1_15) | ~path(V1_15, V2_16, P_17))), inference(cnfTransformation, [status(thm)], [f_123])).
% 4.38/2.21 tff(c_172, plain, (vertex('#skF_9')), inference(resolution, [status(thm)], [c_169, c_38])).
% 4.38/2.21 tff(c_179, plain, $false, inference(negUnitSimplification, [status(thm)], [c_154, c_172])).
% 4.38/2.21 tff(c_180, plain, (~vertex('#skF_10') | ~edge('#skF_11') | ~edge('#skF_12') | ~path('#skF_9', '#skF_10', '#skF_13') | '#skF_10'='#skF_9' | '#skF_11'='#skF_12'), inference(splitRight, [status(thm)], [c_142])).
% 4.38/2.21 tff(c_187, plain, (~path('#skF_9', '#skF_10', '#skF_13')), inference(splitLeft, [status(thm)], [c_180])).
% 4.38/2.21 tff(c_193, plain, (![V1_162, V2_163, SP_164]: (path(V1_162, V2_163, SP_164) | ~shortest_path(V1_162, V2_163, SP_164))), inference(cnfTransformation, [status(thm)], [f_201])).
% 4.38/2.21 tff(c_196, plain, (path('#skF_9', '#skF_10', '#skF_13')), inference(resolution, [status(thm)], [c_146, c_193])).
% 4.38/2.21 tff(c_200, plain, $false, inference(negUnitSimplification, [status(thm)], [c_187, c_196])).
% 4.38/2.21 tff(c_202, plain, (path('#skF_9', '#skF_10', '#skF_13')), inference(splitRight, [status(thm)], [c_180])).
% 4.38/2.21 tff(c_36, plain, (![V2_16, V1_15, P_17]: (vertex(V2_16) | ~path(V1_15, V2_16, P_17))), inference(cnfTransformation, [status(thm)], [f_123])).
% 4.38/2.21 tff(c_211, plain, (vertex('#skF_10')), inference(resolution, [status(thm)], [c_202, c_36])).
% 4.38/2.21 tff(c_201, plain, (~edge('#skF_12') | ~edge('#skF_11') | ~vertex('#skF_10') | '#skF_11'='#skF_12' | '#skF_10'='#skF_9'), inference(splitRight, [status(thm)], [c_180])).
% 4.38/2.21 tff(c_213, plain, (~edge('#skF_12') | ~edge('#skF_11') | '#skF_11'='#skF_12' | '#skF_10'='#skF_9'), inference(demodulation, [status(thm), theory('equality')], [c_211, c_201])).
% 4.38/2.21 tff(c_214, plain, (~edge('#skF_11')), inference(splitLeft, [status(thm)], [c_213])).
% 4.38/2.21 tff(c_144, plain, (precedes('#skF_11', '#skF_12', '#skF_13')), inference(cnfTransformation, [status(thm)], [f_275])).
% 4.38/2.21 tff(c_261, plain, (![P_205, E1_203, E2_204, V2_206, V1_207]: (on_path(E1_203, P_205) | ~precedes(E1_203, E2_204, P_205) | ~path(V1_207, V2_206, P_205))), inference(cnfTransformation, [status(thm)], [f_189])).
% 4.38/2.21 tff(c_264, plain, (![V1_207, V2_206]: (on_path('#skF_11', '#skF_13') | ~path(V1_207, V2_206, '#skF_13'))), inference(resolution, [status(thm)], [c_144, c_261])).
% 4.38/2.21 tff(c_272, plain, (![V1_207, V2_206]: (~path(V1_207, V2_206, '#skF_13'))), inference(splitLeft, [status(thm)], [c_264])).
% 4.38/2.21 tff(c_274, plain, $false, inference(negUnitSimplification, [status(thm)], [c_272, c_202])).
% 4.38/2.21 tff(c_275, plain, (on_path('#skF_11', '#skF_13')), inference(splitRight, [status(thm)], [c_264])).
% 4.38/2.21 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])).
% 4.38/2.21 tff(c_277, plain, (![V1_26, V2_27]: (edge('#skF_11') | ~path(V1_26, V2_27, '#skF_13'))), inference(resolution, [status(thm)], [c_275, c_62])).
% 4.38/2.21 tff(c_280, plain, (![V1_26, V2_27]: (~path(V1_26, V2_27, '#skF_13'))), inference(negUnitSimplification, [status(thm)], [c_214, c_277])).
% 4.38/2.21 tff(c_282, plain, $false, inference(negUnitSimplification, [status(thm)], [c_280, c_202])).
% 4.38/2.21 tff(c_283, plain, (~edge('#skF_12') | '#skF_10'='#skF_9' | '#skF_11'='#skF_12'), inference(splitRight, [status(thm)], [c_213])).
% 4.38/2.21 tff(c_290, plain, (~edge('#skF_12')), inference(splitLeft, [status(thm)], [c_283])).
% 4.38/2.21 tff(c_372, plain, (![V2_258, P_257, V1_259, E2_256, E1_255]: (on_path(E2_256, P_257) | ~precedes(E1_255, E2_256, P_257) | ~path(V1_259, V2_258, P_257))), inference(cnfTransformation, [status(thm)], [f_189])).
% 4.38/2.21 tff(c_375, plain, (![V1_259, V2_258]: (on_path('#skF_12', '#skF_13') | ~path(V1_259, V2_258, '#skF_13'))), inference(resolution, [status(thm)], [c_144, c_372])).
% 4.38/2.21 tff(c_376, plain, (![V1_259, V2_258]: (~path(V1_259, V2_258, '#skF_13'))), inference(splitLeft, [status(thm)], [c_375])).
% 4.38/2.21 tff(c_382, plain, $false, inference(negUnitSimplification, [status(thm)], [c_376, c_202])).
% 4.38/2.21 tff(c_383, plain, (on_path('#skF_12', '#skF_13')), inference(splitRight, [status(thm)], [c_375])).
% 4.38/2.21 tff(c_385, plain, (![V1_26, V2_27]: (edge('#skF_12') | ~path(V1_26, V2_27, '#skF_13'))), inference(resolution, [status(thm)], [c_383, c_62])).
% 4.38/2.21 tff(c_388, plain, (![V1_26, V2_27]: (~path(V1_26, V2_27, '#skF_13'))), inference(negUnitSimplification, [status(thm)], [c_290, c_385])).
% 4.38/2.21 tff(c_390, plain, $false, inference(negUnitSimplification, [status(thm)], [c_388, c_202])).
% 4.38/2.21 tff(c_391, plain, ('#skF_11'='#skF_12' | '#skF_10'='#skF_9'), inference(splitRight, [status(thm)], [c_283])).
% 4.38/2.21 tff(c_397, plain, ('#skF_10'='#skF_9'), inference(splitLeft, [status(thm)], [c_391])).
% 4.38/2.21 tff(c_400, plain, (shortest_path('#skF_9', '#skF_9', '#skF_13')), inference(demodulation, [status(thm), theory('equality')], [c_397, c_146])).
% 4.38/2.21 tff(c_403, plain, $false, inference(negUnitSimplification, [status(thm)], [c_102, c_400])).
% 4.38/2.21 tff(c_404, plain, ('#skF_11'='#skF_12'), inference(splitRight, [status(thm)], [c_391])).
% 4.38/2.21 tff(c_408, plain, (precedes('#skF_12', '#skF_12', '#skF_13')), inference(demodulation, [status(thm), theory('equality')], [c_404, c_144])).
% 4.38/2.21 tff(c_518, plain, (![V1_327, E2_328, P_326, V2_329, E1_330]: (~precedes(E2_328, E1_330, P_326) | ~precedes(E1_330, E2_328, P_326) | ~shortest_path(V1_327, V2_329, P_326))), inference(cnfTransformation, [status(thm)], [f_214])).
% 4.38/2.21 tff(c_520, plain, (![V1_327, V2_329]: (~precedes('#skF_12', '#skF_12', '#skF_13') | ~shortest_path(V1_327, V2_329, '#skF_13'))), inference(resolution, [status(thm)], [c_408, c_518])).
% 4.38/2.21 tff(c_523, plain, (![V1_327, V2_329]: (~shortest_path(V1_327, V2_329, '#skF_13'))), inference(demodulation, [status(thm), theory('equality')], [c_408, c_520])).
% 4.38/2.21 tff(c_525, plain, $false, inference(negUnitSimplification, [status(thm)], [c_523, c_146])).
% 4.38/2.21 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/2.21
% 4.38/2.21 Inference rules
% 4.38/2.21 ----------------------
% 4.38/2.21 #Ref : 0
% 4.38/2.21 #Sup : 67
% 4.38/2.21 #Fact : 0
% 4.38/2.21 #Define : 0
% 4.38/2.21 #Split : 15
% 4.38/2.21 #Chain : 0
% 4.38/2.21 #Close : 0
% 4.38/2.21
% 4.38/2.21 Ordering : KBO
% 4.38/2.21
% 4.38/2.21 Simplification rules
% 4.38/2.21 ----------------------
% 4.38/2.21 #Subsume : 6
% 4.38/2.21 #Demod : 18
% 4.38/2.21 #Tautology : 34
% 4.38/2.21 #SimpNegUnit : 16
% 4.38/2.21 #BackRed : 17
% 4.38/2.21
% 4.38/2.21 #Partial instantiations: 0
% 4.38/2.21 #Strategies tried : 1
% 4.38/2.21
% 4.38/2.21 Timing (in seconds)
% 4.38/2.21 ----------------------
% 4.38/2.21 Preprocessing : 0.64
% 4.38/2.21 Parsing : 0.29
% 4.38/2.21 CNF conversion : 0.05
% 4.38/2.21 Main loop : 0.39
% 4.38/2.21 Inferencing : 0.13
% 4.38/2.21 Reduction : 0.11
% 4.38/2.21 Demodulation : 0.07
% 4.38/2.21 BG Simplification : 0.03
% 4.38/2.21 Subsumption : 0.09
% 4.38/2.21 Abstraction : 0.02
% 4.38/2.21 MUC search : 0.00
% 4.38/2.21 Cooper : 0.00
% 4.38/2.21 Total : 1.09
% 4.38/2.21 Index Insertion : 0.00
% 4.38/2.21 Index Deletion : 0.00
% 4.38/2.21 Index Matching : 0.00
% 4.38/2.21 BG Taut test : 0.00
%------------------------------------------------------------------------------