%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.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 : Fri May 19 11:12:51 EDT 2023

% Result   : Theorem 47.70s 47.03s
% Output   : Proof 47.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n007.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 : Thu May 18 20:23:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 47.70/47.03  
% 47.70/47.03  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 47.70/47.03  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.70/47.03  %-----------------------------------------------------
% 47.70/47.03  ncf(matrix, plain, [(593 ^ _114952) ^ [] : [less_or_equal(minus(length_of(587 ^ []), n1), number_of_in(triangles, graph))], (591 ^ _114952) ^ [] : [-(shortest_path(588 ^ [], 589 ^ [], 587 ^ []))], (586 ^ _114952) ^ [] : [-(complete)], !, (518 ^ _94307) ^ [_112549, _112551, _112553] : [-(triangle(_112553, _112551, _112549)), edge(_112553), edge(_112551), edge(_112549), sequential(_112553, _112551), sequential(_112551, _112549), sequential(_112549, _112553)], (184 ^ _94307) ^ [_100438, _100440] : [_100440 = _100438, -(head_of(_100440) = head_of(_100438))], (2 ^ _94307) ^ [_94431] : [-(_94431 = _94431)], (426 ^ _94307) ^ [_108983, _108985, _108987] : [path(_108985, _108983, _108987), 429 ^ _94307 : [(430 ^ _94307) ^ [_109178, _109180] : [precedes(_109180, _109178, _108987), 433 ^ _94307 : [(438 ^ _94307) ^ [] : [448 ^ _94307 : [(453 ^ _94307) ^ [] : [sequential(_109180, _109178)], (451 ^ _94307) ^ [] : [-(precedes(447 ^ [_108983, _108985, _108987, _109178, _109180], _109178, _108987))], (449 ^ _94307) ^ [] : [-(sequential(_109180, 447 ^ [_108983, _108985, _108987, _109178, _109180]))]], 439 ^ _94307 : [(442 ^ _94307) ^ [_109621] : [sequential(_109180, _109621), precedes(_109621, _109178, _108987)], (440 ^ _94307) ^ [] : [-(sequential(_109180, _109178))]]], (436 ^ _94307) ^ [] : [-(on_path(_109178, _108987))], (434 ^ _94307) ^ [] : [-(on_path(_109180, _108987))]]]]], (4 ^ _94307) ^ [_94538, _94540] : [_94540 = _94538, -(_94538 = _94540)], (544 ^ _94307) ^ [_113242, _113244, _113246] : [path(_113246, _113244, _113242), -(length_of(_113242) = number_of_in(edges, _113242))], (574 ^ _94307) ^ [_114538, _114540] : [-(less_or_equal(number_of_in(_114540, _114538), number_of_in(_114540, graph)))], (372 ^ _94307) ^ [_107191, _107193] : [sequential(_107193, _107191), 375 ^ _94307 : [(378 ^ _94307) ^ [] : [-(edge(_107191))], (380 ^ _94307) ^ [] : [_107193 = _107191], (382 ^ _94307) ^ [] : [-(head_of(_107193) = tail_of(_107191))], (376 ^ _94307) ^ [] : [-(edge(_107193))]]], (469 ^ _94307) ^ [_110721, _110723, _110725] : [-(shortest_path(_110725, _110723, _110721)), path(_110725, _110723, _110721), -(_110725 = _110723), 479 ^ _94307 : [(482 ^ _94307) ^ [] : [less_or_equal(length_of(_110721), length_of(478 ^ [_110721, _110723, _110725]))], (480 ^ _94307) ^ [] : [-(path(_110725, _110723, 478 ^ [_110721, _110723, _110725]))]]], (216 ^ _94307) ^ [_101600] : [edge(_101600), head_of(_101600) = tail_of(_101600)], (136 ^ _94307) ^ [_98860, _98862, _98864, _98866, _98868, _98870] : [-(shortest_path(_98868, _98864, _98860)), shortest_path(_98870, _98866, _98862), _98870 = _98868, _98866 = _98864, _98862 = _98860], (34 ^ _94307) ^ [_95499, _95501] : [-(vertex(_95499)), _95501 = _95499, vertex(_95501)], (402 ^ _94307) ^ [_108081, _108083, _108085] : [path(_108083, _108081, _108085), 405 ^ _94307 : [(406 ^ _94307) ^ [_108274, _108276] : [-(precedes(_108276, _108274, _108085)), on_path(_108276, _108085), on_path(_108274, _108085), 415 ^ _94307 : [(418 ^ _94307) ^ [_108651] : [sequential(_108276, _108651), precedes(_108651, _108274, _108085)], (416 ^ _94307) ^ [] : [sequential(_108276, _108274)]]]]], (339 ^ _94307) ^ [_105959, _105961, _105963, _105965] : [346 ^ _94307 : [(351 ^ _94307) ^ [] : [-(in_path(tail_of(_105959), _105961))], (349 ^ _94307) ^ [] : [-(in_path(head_of(_105959), _105961))], (347 ^ _94307) ^ [] : [-(edge(_105959))]], path(_105965, _105963, _105961), on_path(_105959, _105961)], (486 ^ _94307) ^ [_111324, _111326, _111328, _111330, _111332] : [shortest_path(_111332, _111330, _111324), precedes(_111328, _111326, _111324), 493 ^ _94307 : [(494 ^ _94307) ^ [_111617] : [tail_of(_111617) = tail_of(_111328), head_of(_111617) = head_of(_111326)], (500 ^ _94307) ^ [] : [precedes(_111326, _111328, _111324)]]], (154 ^ _94307) ^ [_99421, _99423, _99425, _99427] : [-(less_or_equal(_99425, _99421)), less_or_equal(_99427, _99423), _99427 = _99425, _99423 = _99421], (556 ^ _94307) ^ [_113732, _113734, _113736] : [-(number_of_in(sequential_pairs, _113736) = number_of_in(triangles, _113736)), path(_113734, _113732, _113736), 563 ^ _94307 : [(566 ^ _94307) ^ [] : [-(on_path(562 ^ [_113732, _113734, _113736], _113736))], (568 ^ _94307) ^ [] : [-(sequential(561 ^ [_113732, _113734, _113736], 562 ^ [_113732, _113734, _113736]))], (570 ^ _94307) ^ [_114352] : [triangle(561 ^ [_113732, _113734, _113736], 562 ^ [_113732, _113734, _113736], _114352)], (564 ^ _94307) ^ [] : [-(on_path(561 ^ [_113732, _113734, _113736], _113736))]]], (168 ^ _94307) ^ [_99889, _99891, _99893, _99895] : [-(path_cons(_99895, _99891) = path_cons(_99893, _99889)), _99895 = _99893, _99891 = _99889], (178 ^ _94307) ^ [_100220, _100222] : [_100222 = _100220, -(tail_of(_100222) = tail_of(_100220))], (303 ^ _94307) ^ [_104424, _104426, _104428] : [path(_104428, _104426, _104424), 306 ^ _94307 : [(307 ^ _94307) ^ [] : [-(vertex(_104428))], (312 ^ _94307) ^ [] : [-(edge(310 ^ [_104424, _104426, _104428]))], (316 ^ _94307) ^ [] : [317 ^ _94307 : [(322 ^ _94307) ^ [_105213] : [path(head_of(310 ^ [_104424, _104426, _104428]), _104426, _105213), _104424 = path_cons(310 ^ [_104424, _104426, _104428], _105213)], (320 ^ _94307) ^ [] : [-(_104424 = path_cons(310 ^ [_104424, _104426, _104428], empty))], (318 ^ _94307) ^ [] : [-(_104426 = head_of(310 ^ [_104424, _104426, _104428]))]], 328 ^ _94307 : [(333 ^ _94307) ^ [] : [_104426 = head_of(310 ^ [_104424, _104426, _104428]), _104424 = path_cons(310 ^ [_104424, _104426, _104428], empty)], (331 ^ _94307) ^ [] : [-(_104424 = path_cons(310 ^ [_104424, _104426, _104428], 327 ^ [_104424, _104426, _104428]))], (329 ^ _94307) ^ [] : [-(path(head_of(310 ^ [_104424, _104426, _104428]), _104426, 327 ^ [_104424, _104426, _104428]))]]], (314 ^ _94307) ^ [] : [-(_104428 = tail_of(310 ^ [_104424, _104426, _104428]))], (309 ^ _94307) ^ [] : [-(vertex(_104426))]]], (90 ^ _94307) ^ [_97335, _97337, _97339, _97341] : [-(on_path(_97339, _97335)), on_path(_97341, _97337), _97341 = _97339, _97337 = _97335], (62 ^ _94307) ^ [_96403, _96405] : [-(edge(_96403)), _96405 = _96403, edge(_96405)], (20 ^ _94307) ^ [_95083, _95085, _95087, _95089] : [-(in_path(_95087, _95083)), in_path(_95089, _95085), _95089 = _95087, _95085 = _95083], (206 ^ _94307) ^ [_101241, _101243, _101245, _101247] : [-(number_of_in(_101247, _101243) = number_of_in(_101245, _101241)), _101247 = _101245, _101243 = _101241], (190 ^ _94307) ^ [_100684, _100686, _100688, _100690] : [-(minus(_100690, _100686) = minus(_100688, _100684)), _100690 = _100688, _100686 = _100684], (10 ^ _94307) ^ [_94742, _94744, _94746] : [-(_94746 = _94742), _94746 = _94744, _94744 = _94742], (44 ^ _94307) ^ [_95850, _95852, _95854, _95856, _95858, _95860] : [-(precedes(_95858, _95854, _95850)), precedes(_95860, _95856, _95852), _95860 = _95858, _95856 = _95854, _95852 = _95850], (271 ^ _94307) ^ [_103346, _103348, _103350] : [-(path(_103350, _103348, _103346)), vertex(_103350), vertex(_103348), 280 ^ _94307 : [(281 ^ _94307) ^ [_103656] : [edge(_103656), _103350 = tail_of(_103656), 288 ^ _94307 : [(295 ^ _94307) ^ [_104090] : [path(head_of(_103656), _103348, _104090), _103346 = path_cons(_103656, _104090)], (289 ^ _94307) ^ [] : [_103348 = head_of(_103656), _103346 = path_cons(_103656, empty)]]]]], (550 ^ _94307) ^ [_113484, _113486, _113488] : [path(_113488, _113486, _113484), -(number_of_in(sequential_pairs, _113484) = minus(length_of(_113484), n1))], (384 ^ _94307) ^ [_107581, _107583] : [-(sequential(_107583, _107581)), edge(_107583), edge(_107581), -(_107583 = _107581), head_of(_107583) = tail_of(_107581)], (118 ^ _94307) ^ [_98251, _98253, _98255, _98257, _98259, _98261] : [-(triangle(_98259, _98255, _98251)), triangle(_98261, _98257, _98253), _98261 = _98259, _98257 = _98255, _98253 = _98251], (353 ^ _94307) ^ [_106471, _106473, _106475, _106477] : [path(_106477, _106475, _106473), in_path(_106471, _106473), 360 ^ _94307 : [(366 ^ _94307) ^ [] : [-(_106471 = head_of(362 ^ [_106471, _106473, _106475, _106477])), -(_106471 = tail_of(362 ^ [_106471, _106473, _106475, _106477]))], (364 ^ _94307) ^ [] : [-(on_path(362 ^ [_106471, _106473, _106475, _106477], _106473))], (361 ^ _94307) ^ [] : [-(vertex(_106471))]]], (72 ^ _94307) ^ [_96754, _96756, _96758, _96760, _96762, _96764] : [-(path(_96762, _96758, _96754)), path(_96764, _96760, _96756), _96764 = _96762, _96760 = _96758, _96756 = _96754], (455 ^ _94307) ^ [_110223, _110225, _110227] : [shortest_path(_110227, _110225, _110223), 458 ^ _94307 : [(463 ^ _94307) ^ [_110522] : [path(_110227, _110225, _110522), -(less_or_equal(length_of(_110223), length_of(_110522)))], (461 ^ _94307) ^ [] : [_110227 = _110225], (459 ^ _94307) ^ [] : [-(path(_110227, _110225, _110223))]]], (230 ^ _94307) ^ [] : [complete, 233 ^ _94307 : [(234 ^ _94307) ^ [_102138, _102140] : [vertex(_102140), vertex(_102138), -(_102140 = _102138), 246 ^ _94307 : [(249 ^ _94307) ^ [] : [250 ^ _94307 : [(255 ^ _94307) ^ [] : [_102138 = head_of(245 ^ [_102138, _102140]), _102140 = tail_of(245 ^ [_102138, _102140])], (253 ^ _94307) ^ [] : [-(_102138 = tail_of(245 ^ [_102138, _102140]))], (251 ^ _94307) ^ [] : [-(_102140 = head_of(245 ^ [_102138, _102140]))]], 260 ^ _94307 : [(265 ^ _94307) ^ [] : [_102140 = head_of(245 ^ [_102138, _102140]), _102138 = tail_of(245 ^ [_102138, _102140])], (263 ^ _94307) ^ [] : [-(_102140 = tail_of(245 ^ [_102138, _102140]))], (261 ^ _94307) ^ [] : [-(_102138 = head_of(245 ^ [_102138, _102140]))]]], (247 ^ _94307) ^ [] : [-(edge(245 ^ [_102138, _102140]))]]]]], (200 ^ _94307) ^ [_101015, _101017] : [_101017 = _101015, -(length_of(_101017) = length_of(_101015))], (576 ^ _94307) ^ [] : [complete, 579 ^ _94307 : [(580 ^ _94307) ^ [_114709, _114711, _114713] : [shortest_path(_114711, _114709, _114713), -(number_of_in(sequential_pairs, _114713) = number_of_in(triangles, _114713))]]], (222 ^ _94307) ^ [_101797] : [edge(_101797), 225 ^ _94307 : [(228 ^ _94307) ^ [] : [-(vertex(tail_of(_101797)))], (226 ^ _94307) ^ [] : [-(vertex(head_of(_101797)))]]], (104 ^ _94307) ^ [_97779, _97781, _97783, _97785] : [-(sequential(_97783, _97779)), sequential(_97785, _97781), _97785 = _97783, _97781 = _97779], (502 ^ _94307) ^ [_112004, _112006, _112008] : [triangle(_112008, _112006, _112004), 505 ^ _94307 : [(508 ^ _94307) ^ [] : [-(edge(_112006))], (506 ^ _94307) ^ [] : [-(edge(_112008))], (516 ^ _94307) ^ [] : [-(sequential(_112004, _112008))], (512 ^ _94307) ^ [] : [-(sequential(_112008, _112006))], (514 ^ _94307) ^ [] : [-(sequential(_112006, _112004))], (510 ^ _94307) ^ [] : [-(edge(_112004))]]]], input).
% 47.70/47.03  ncf('1',plain,[-(shortest_path(588 ^ [], 589 ^ [], 587 ^ []))],start(591 ^ 0)).
% 47.70/47.03  ncf('1.1',plain,[shortest_path(588 ^ [], 589 ^ [], 587 ^ []), 459 : -(path(588 ^ [], 589 ^ [], 587 ^ []))],extension(455 ^ 1,bind([[_110223, _110225, _110227], [587 ^ [], 589 ^ [], 588 ^ []]]))).
% 47.70/47.03  ncf('1.1.1',plain,[path(588 ^ [], 589 ^ [], 587 ^ []), -(number_of_in(sequential_pairs, 587 ^ []) = minus(length_of(587 ^ []), n1))],extension(550 ^ 4,bind([[_113484, _113486, _113488], [587 ^ [], 589 ^ [], 588 ^ []]]))).
% 47.70/47.03  ncf('1.1.1.1',plain,[number_of_in(sequential_pairs, 587 ^ []) = minus(length_of(587 ^ []), n1), -(number_of_in(triangles, 587 ^ []) = minus(length_of(587 ^ []), n1)), number_of_in(triangles, 587 ^ []) = number_of_in(sequential_pairs, 587 ^ [])],extension(10 ^ 5,bind([[_94742, _94744, _94746], [minus(length_of(587 ^ []), n1), number_of_in(sequential_pairs, 587 ^ []), number_of_in(triangles, 587 ^ [])]]))).
% 47.70/47.03  ncf('1.1.1.1.1',plain,[number_of_in(triangles, 587 ^ []) = minus(length_of(587 ^ []), n1), -(less_or_equal(minus(length_of(587 ^ []), n1), number_of_in(triangles, graph))), less_or_equal(number_of_in(triangles, 587 ^ []), number_of_in(triangles, graph)), number_of_in(triangles, graph) = number_of_in(triangles, graph)],extension(154 ^ 6,bind([[_99421, _99423, _99425, _99427], [number_of_in(triangles, graph), number_of_in(triangles, graph), minus(length_of(587 ^ []), n1), number_of_in(triangles, 587 ^ [])]]))).
% 47.70/47.03  ncf('1.1.1.1.1.1',plain,[less_or_equal(minus(length_of(587 ^ []), n1), number_of_in(triangles, graph))],extension(593 ^ 7)).
% 47.70/47.03  ncf('1.1.1.1.1.2',plain,[-(less_or_equal(number_of_in(triangles, 587 ^ []), number_of_in(triangles, graph)))],extension(574 ^ 7,bind([[_114538, _114540], [587 ^ [], triangles]]))).
% 47.70/47.03  ncf('1.1.1.1.1.3',plain,[-(number_of_in(triangles, graph) = number_of_in(triangles, graph))],extension(2 ^ 7,bind([[_94431], [number_of_in(triangles, graph)]]))).
% 47.70/47.03  ncf('1.1.1.1.2',plain,[-(number_of_in(triangles, 587 ^ []) = number_of_in(sequential_pairs, 587 ^ [])), number_of_in(sequential_pairs, 587 ^ []) = number_of_in(triangles, 587 ^ [])],extension(4 ^ 6,bind([[_94538, _94540], [number_of_in(triangles, 587 ^ []), number_of_in(sequential_pairs, 587 ^ [])]]))).
% 47.70/47.03  ncf('1.1.1.1.2.1',plain,[-(number_of_in(sequential_pairs, 587 ^ []) = number_of_in(triangles, 587 ^ [])), 580 : shortest_path(588 ^ [], 589 ^ [], 587 ^ []), 580 : complete],extension(576 ^ 7,bind([[_114709, _114711, _114713], [589 ^ [], 588 ^ [], 587 ^ []]]))).
% 47.70/47.03  ncf('1.1.1.1.2.1.1',plain,[-(shortest_path(588 ^ [], 589 ^ [], 587 ^ []))],reduction('1')).
% 47.70/47.03  ncf('1.1.1.1.2.1.2',plain,[-(complete)],extension(586 ^ 8)).
% 47.70/47.03  %-----------------------------------------------------
% 47.70/47.03  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------