%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 11:12:52 EDT 2023

% Result   : Theorem 0.34s 1.37s
% Output   : Proof 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 20:32:18 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.34/1.37  
% 0.34/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.34/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  ncf(matrix, plain, [(576 ^ _89994) ^ [] : [-(complete)], (598 ^ _89994) ^ [] : [number_of_in(sequential_pairs, 577 ^ []) = number_of_in(triangles, 577 ^ [])], (581 ^ _89994) ^ [] : [-(path(578 ^ [], 579 ^ [], 577 ^ []))], (583 ^ _89994) ^ [_110814, _110816] : [-(triangle(_110816, _110814, 594 ^ [_110814, _110816])), on_path(_110816, 577 ^ []), on_path(_110814, 577 ^ []), sequential(_110816, _110814)], (168 ^ _89994) ^ [_95596, _95598, _95600, _95602] : [-(path_cons(_95602, _95598) = path_cons(_95600, _95596)), _95602 = _95600, _95598 = _95596], (178 ^ _89994) ^ [_95927, _95929] : [_95929 = _95927, -(tail_of(_95929) = tail_of(_95927))], (184 ^ _89994) ^ [_96145, _96147] : [_96147 = _96145, -(head_of(_96147) = head_of(_96145))], (190 ^ _89994) ^ [_96391, _96393, _96395, _96397] : [-(minus(_96397, _96393) = minus(_96395, _96391)), _96397 = _96395, _96393 = _96391], (200 ^ _89994) ^ [_96722, _96724] : [_96724 = _96722, -(length_of(_96724) = length_of(_96722))], (206 ^ _89994) ^ [_96948, _96950, _96952, _96954] : [-(number_of_in(_96954, _96950) = number_of_in(_96952, _96948)), _96954 = _96952, _96950 = _96948], (2 ^ _89994) ^ [_90138] : [-(_90138 = _90138)], (4 ^ _89994) ^ [_90245, _90247] : [_90247 = _90245, -(_90245 = _90247)], (10 ^ _89994) ^ [_90449, _90451, _90453] : [-(_90453 = _90449), _90453 = _90451, _90451 = _90449], (20 ^ _89994) ^ [_90790, _90792, _90794, _90796] : [-(in_path(_90794, _90790)), in_path(_90796, _90792), _90796 = _90794, _90792 = _90790], (34 ^ _89994) ^ [_91206, _91208] : [-(vertex(_91206)), _91208 = _91206, vertex(_91208)], (44 ^ _89994) ^ [_91557, _91559, _91561, _91563, _91565, _91567] : [-(shortest_path(_91565, _91561, _91557)), shortest_path(_91567, _91563, _91559), _91567 = _91565, _91563 = _91561, _91559 = _91557], (62 ^ _89994) ^ [_92166, _92168, _92170, _92172, _92174, _92176] : [-(precedes(_92174, _92170, _92166)), precedes(_92176, _92172, _92168), _92176 = _92174, _92172 = _92170, _92168 = _92166], (80 ^ _89994) ^ [_92719, _92721] : [-(edge(_92719)), _92721 = _92719, edge(_92721)], (90 ^ _89994) ^ [_93042, _93044, _93046, _93048] : [-(less_or_equal(_93046, _93042)), less_or_equal(_93048, _93044), _93048 = _93046, _93044 = _93042], (104 ^ _89994) ^ [_93514, _93516, _93518, _93520, _93522, _93524] : [-(path(_93522, _93518, _93514)), path(_93524, _93520, _93516), _93524 = _93522, _93520 = _93518, _93516 = _93514], (122 ^ _89994) ^ [_94095, _94097, _94099, _94101] : [-(on_path(_94099, _94095)), on_path(_94101, _94097), _94101 = _94099, _94097 = _94095], (136 ^ _89994) ^ [_94539, _94541, _94543, _94545] : [-(sequential(_94543, _94539)), sequential(_94545, _94541), _94545 = _94543, _94541 = _94539], (150 ^ _89994) ^ [_94991, _94993, _94995, _94997, _94999, _95001] : [-(triangle(_94999, _94995, _94991)), triangle(_95001, _94997, _94993), _95001 = _94999, _94997 = _94995, _94993 = _94991], (544 ^ _89994) ^ [_108949, _108951, _108953] : [path(_108953, _108951, _108949), -(length_of(_108949) = number_of_in(edges, _108949))], (550 ^ _89994) ^ [_109191, _109193, _109195] : [path(_109195, _109193, _109191), -(number_of_in(sequential_pairs, _109191) = minus(length_of(_109191), n1))], (574 ^ _89994) ^ [_110225, _110227] : [-(less_or_equal(number_of_in(_110227, _110225), number_of_in(_110227, graph)))], (556 ^ _89994) ^ [_109439, _109441, _109443] : [-(number_of_in(sequential_pairs, _109443) = number_of_in(triangles, _109443)), path(_109441, _109439, _109443), 563 ^ _89994 : [(564 ^ _89994) ^ [] : [-(on_path(561 ^ [_109439, _109441, _109443], _109443))], (566 ^ _89994) ^ [] : [-(on_path(562 ^ [_109439, _109441, _109443], _109443))], (568 ^ _89994) ^ [] : [-(sequential(561 ^ [_109439, _109441, _109443], 562 ^ [_109439, _109441, _109443]))], (570 ^ _89994) ^ [_110059] : [triangle(561 ^ [_109439, _109441, _109443], 562 ^ [_109439, _109441, _109443], _110059)]]], (502 ^ _89994) ^ [_107711, _107713, _107715] : [triangle(_107715, _107713, _107711), 505 ^ _89994 : [(506 ^ _89994) ^ [] : [-(edge(_107715))], (508 ^ _89994) ^ [] : [-(edge(_107713))], (510 ^ _89994) ^ [] : [-(edge(_107711))], (512 ^ _89994) ^ [] : [-(sequential(_107715, _107713))], (514 ^ _89994) ^ [] : [-(sequential(_107713, _107711))], (516 ^ _89994) ^ [] : [-(sequential(_107711, _107715))]]], (518 ^ _89994) ^ [_108256, _108258, _108260] : [-(triangle(_108260, _108258, _108256)), edge(_108260), edge(_108258), edge(_108256), sequential(_108260, _108258), sequential(_108258, _108256), sequential(_108256, _108260)], (216 ^ _89994) ^ [_97307] : [edge(_97307), head_of(_97307) = tail_of(_97307)], (222 ^ _89994) ^ [_97504] : [edge(_97504), 225 ^ _89994 : [(226 ^ _89994) ^ [] : [-(vertex(head_of(_97504)))], (228 ^ _89994) ^ [] : [-(vertex(tail_of(_97504)))]]], (230 ^ _89994) ^ [] : [complete, 233 ^ _89994 : [(234 ^ _89994) ^ [_97845, _97847] : [vertex(_97847), vertex(_97845), -(_97847 = _97845), 246 ^ _89994 : [(247 ^ _89994) ^ [] : [-(edge(245 ^ [_97845, _97847]))], (249 ^ _89994) ^ [] : [250 ^ _89994 : [(251 ^ _89994) ^ [] : [-(_97847 = head_of(245 ^ [_97845, _97847]))], (253 ^ _89994) ^ [] : [-(_97845 = tail_of(245 ^ [_97845, _97847]))], (255 ^ _89994) ^ [] : [_97845 = head_of(245 ^ [_97845, _97847]), _97847 = tail_of(245 ^ [_97845, _97847])]], 260 ^ _89994 : [(261 ^ _89994) ^ [] : [-(_97845 = head_of(245 ^ [_97845, _97847]))], (263 ^ _89994) ^ [] : [-(_97847 = tail_of(245 ^ [_97845, _97847]))], (265 ^ _89994) ^ [] : [_97847 = head_of(245 ^ [_97845, _97847]), _97845 = tail_of(245 ^ [_97845, _97847])]]]]]]], (271 ^ _89994) ^ [_99053, _99055, _99057] : [-(path(_99057, _99055, _99053)), vertex(_99057), vertex(_99055), 280 ^ _89994 : [(281 ^ _89994) ^ [_99363] : [edge(_99363), _99057 = tail_of(_99363), 288 ^ _89994 : [(289 ^ _89994) ^ [] : [_99055 = head_of(_99363), _99053 = path_cons(_99363, empty)], (295 ^ _89994) ^ [_99797] : [path(head_of(_99363), _99055, _99797), _99053 = path_cons(_99363, _99797)]]]]], (303 ^ _89994) ^ [_100131, _100133, _100135] : [path(_100135, _100133, _100131), 306 ^ _89994 : [(307 ^ _89994) ^ [] : [-(vertex(_100135))], (309 ^ _89994) ^ [] : [-(vertex(_100133))], (312 ^ _89994) ^ [] : [-(edge(310 ^ [_100131, _100133, _100135]))], (314 ^ _89994) ^ [] : [-(_100135 = tail_of(310 ^ [_100131, _100133, _100135]))], (316 ^ _89994) ^ [] : [317 ^ _89994 : [(318 ^ _89994) ^ [] : [-(_100133 = head_of(310 ^ [_100131, _100133, _100135]))], (320 ^ _89994) ^ [] : [-(_100131 = path_cons(310 ^ [_100131, _100133, _100135], empty))], (322 ^ _89994) ^ [_100920] : [path(head_of(310 ^ [_100131, _100133, _100135]), _100133, _100920), _100131 = path_cons(310 ^ [_100131, _100133, _100135], _100920)]], 328 ^ _89994 : [(329 ^ _89994) ^ [] : [-(path(head_of(310 ^ [_100131, _100133, _100135]), _100133, 327 ^ [_100131, _100133, _100135]))], (331 ^ _89994) ^ [] : [-(_100131 = path_cons(310 ^ [_100131, _100133, _100135], 327 ^ [_100131, _100133, _100135]))], (333 ^ _89994) ^ [] : [_100133 = head_of(310 ^ [_100131, _100133, _100135]), _100131 = path_cons(310 ^ [_100131, _100133, _100135], empty)]]]]], (339 ^ _89994) ^ [_101666, _101668, _101670, _101672] : [346 ^ _89994 : [(347 ^ _89994) ^ [] : [-(edge(_101666))], (349 ^ _89994) ^ [] : [-(in_path(head_of(_101666), _101668))], (351 ^ _89994) ^ [] : [-(in_path(tail_of(_101666), _101668))]], path(_101672, _101670, _101668), on_path(_101666, _101668)], (353 ^ _89994) ^ [_102178, _102180, _102182, _102184] : [path(_102184, _102182, _102180), in_path(_102178, _102180), 360 ^ _89994 : [(361 ^ _89994) ^ [] : [-(vertex(_102178))], (364 ^ _89994) ^ [] : [-(on_path(362 ^ [_102178, _102180, _102182, _102184], _102180))], (366 ^ _89994) ^ [] : [-(_102178 = head_of(362 ^ [_102178, _102180, _102182, _102184])), -(_102178 = tail_of(362 ^ [_102178, _102180, _102182, _102184]))]]], (372 ^ _89994) ^ [_102898, _102900] : [sequential(_102900, _102898), 375 ^ _89994 : [(376 ^ _89994) ^ [] : [-(edge(_102900))], (378 ^ _89994) ^ [] : [-(edge(_102898))], (380 ^ _89994) ^ [] : [_102900 = _102898], (382 ^ _89994) ^ [] : [-(head_of(_102900) = tail_of(_102898))]]], (384 ^ _89994) ^ [_103288, _103290] : [-(sequential(_103290, _103288)), edge(_103290), edge(_103288), -(_103290 = _103288), head_of(_103290) = tail_of(_103288)], (402 ^ _89994) ^ [_103788, _103790, _103792] : [path(_103790, _103788, _103792), 405 ^ _89994 : [(406 ^ _89994) ^ [_103981, _103983] : [-(precedes(_103983, _103981, _103792)), on_path(_103983, _103792), on_path(_103981, _103792), 415 ^ _89994 : [(416 ^ _89994) ^ [] : [sequential(_103983, _103981)], (418 ^ _89994) ^ [_104358] : [sequential(_103983, _104358), precedes(_104358, _103981, _103792)]]]]], (426 ^ _89994) ^ [_104690, _104692, _104694] : [path(_104692, _104690, _104694), 429 ^ _89994 : [(430 ^ _89994) ^ [_104885, _104887] : [precedes(_104887, _104885, _104694), 433 ^ _89994 : [(434 ^ _89994) ^ [] : [-(on_path(_104887, _104694))], (436 ^ _89994) ^ [] : [-(on_path(_104885, _104694))], (438 ^ _89994) ^ [] : [448 ^ _89994 : [(449 ^ _89994) ^ [] : [-(sequential(_104887, 447 ^ [_104690, _104692, _104694, _104885, _104887]))], (451 ^ _89994) ^ [] : [-(precedes(447 ^ [_104690, _104692, _104694, _104885, _104887], _104885, _104694))], (453 ^ _89994) ^ [] : [sequential(_104887, _104885)]], 439 ^ _89994 : [(440 ^ _89994) ^ [] : [-(sequential(_104887, _104885))], (442 ^ _89994) ^ [_105328] : [sequential(_104887, _105328), precedes(_105328, _104885, _104694)]]]]]]], (486 ^ _89994) ^ [_107031, _107033, _107035, _107037, _107039] : [shortest_path(_107039, _107037, _107031), precedes(_107035, _107033, _107031), 493 ^ _89994 : [(500 ^ _89994) ^ [] : [precedes(_107033, _107035, _107031)], (494 ^ _89994) ^ [_107324] : [tail_of(_107324) = tail_of(_107035), head_of(_107324) = head_of(_107033)]]], (455 ^ _89994) ^ [_105930, _105932, _105934] : [shortest_path(_105934, _105932, _105930), 458 ^ _89994 : [(459 ^ _89994) ^ [] : [-(path(_105934, _105932, _105930))], (461 ^ _89994) ^ [] : [_105934 = _105932], (463 ^ _89994) ^ [_106229] : [path(_105934, _105932, _106229), -(less_or_equal(length_of(_105930), length_of(_106229)))]]], (469 ^ _89994) ^ [_106428, _106430, _106432] : [-(shortest_path(_106432, _106430, _106428)), path(_106432, _106430, _106428), -(_106432 = _106430), 479 ^ _89994 : [(480 ^ _89994) ^ [] : [-(path(_106432, _106430, 478 ^ [_106428, _106430, _106432]))], (482 ^ _89994) ^ [] : [less_or_equal(length_of(_106428), length_of(478 ^ [_106428, _106430, _106432]))]]]], input).
% 0.34/1.37  ncf('1',plain,[number_of_in(sequential_pairs, 577 ^ []) = number_of_in(triangles, 577 ^ [])],start(598 ^ 0)).
% 0.34/1.37  ncf('1.1',plain,[-(number_of_in(sequential_pairs, 577 ^ []) = number_of_in(triangles, 577 ^ [])), path(578 ^ [], 579 ^ [], 577 ^ []), 564 : -(on_path(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 577 ^ []))],extension(556 ^ 1,bind([[_109439, _109441, _109443], [579 ^ [], 578 ^ [], 577 ^ []]]))).
% 0.34/1.37  ncf('1.1.1',plain,[-(path(578 ^ [], 579 ^ [], 577 ^ []))],extension(581 ^ 2)).
% 0.34/1.37  ncf('1.1.2',plain,[on_path(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 577 ^ []), -(triangle(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 594 ^ [562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 561 ^ [579 ^ [], 578 ^ [], 577 ^ []]])), on_path(562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 577 ^ []), sequential(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 562 ^ [579 ^ [], 578 ^ [], 577 ^ []])],extension(583 ^ 4,bind([[_110814, _110816], [562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 561 ^ [579 ^ [], 578 ^ [], 577 ^ []]]]))).
% 0.34/1.37  ncf('1.1.2.1',plain,[triangle(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 594 ^ [562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 561 ^ [579 ^ [], 578 ^ [], 577 ^ []]])],extension(570 ^ 5,bind([[_110059], [594 ^ [562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 561 ^ [579 ^ [], 578 ^ [], 577 ^ []]]]]))).
% 0.34/1.37  ncf('1.1.2.2',plain,[-(on_path(562 ^ [579 ^ [], 578 ^ [], 577 ^ []], 577 ^ []))],extension(566 ^ 5)).
% 0.34/1.37  ncf('1.1.2.3',plain,[-(sequential(561 ^ [579 ^ [], 578 ^ [], 577 ^ []], 562 ^ [579 ^ [], 578 ^ [], 577 ^ []]))],extension(568 ^ 5)).
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------