%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n022.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 219.90s 211.86s
% Output   : Proof 219.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem  : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.09/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 20:31:02 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 219.90/211.86  
% 219.90/211.86  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 219.90/211.86  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 219.90/211.86  %-----------------------------------------------------
% 219.90/211.86  ncf(matrix, plain, [(587 ^ _134182) ^ [_134821] : [edge(_134821), tail_of(_134821) = head_of(580 ^ []), head_of(_134821) = tail_of(579 ^ [])], (576 ^ _134182) ^ [] : [-(complete)], (585 ^ _134182) ^ [] : [-(precedes(579 ^ [], 580 ^ [], 581 ^ []))], (583 ^ _134182) ^ [] : [-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))], !, (372 ^ _113848) ^ [_126732, _126734] : [sequential(_126734, _126732), 375 ^ _113848 : [(382 ^ _113848) ^ [] : [-(head_of(_126734) = tail_of(_126732))], (376 ^ _113848) ^ [] : [-(edge(_126734))], (380 ^ _113848) ^ [] : [_126734 = _126732], (378 ^ _113848) ^ [] : [-(edge(_126732))]]], (122 ^ _113848) ^ [_117941, _117943, _117945, _117947, _117949, _117951] : [-(shortest_path(_117949, _117945, _117941)), shortest_path(_117951, _117947, _117943), _117951 = _117949, _117947 = _117945, _117943 = _117941], (62 ^ _113848) ^ [_115972, _115974, _115976, _115978] : [-(on_path(_115976, _115972)), on_path(_115978, _115974), _115978 = _115976, _115974 = _115972], (204 ^ _113848) ^ [_120697, _120699] : [_120699 = _120697, -(head_of(_120699) = head_of(_120697))], (544 ^ _113848) ^ [_132783, _132785, _132787] : [path(_132787, _132785, _132783), -(length_of(_132783) = number_of_in(edges, _132783))], (194 ^ _113848) ^ [_120366, _120368, _120370, _120372] : [-(number_of_in(_120372, _120368) = number_of_in(_120370, _120366)), _120372 = _120370, _120368 = _120366], (140 ^ _113848) ^ [_118550, _118552, _118554, _118556, _118558, _118560] : [-(precedes(_118558, _118554, _118550)), precedes(_118560, _118556, _118552), _118560 = _118558, _118556 = _118554, _118552 = _118550], (574 ^ _113848) ^ [_134059, _134061] : [-(less_or_equal(number_of_in(_134061, _134059), number_of_in(_134061, graph)))], (108 ^ _113848) ^ [_117469, _117471, _117473, _117475] : [-(less_or_equal(_117473, _117469)), less_or_equal(_117475, _117471), _117475 = _117473, _117471 = _117469], (4 ^ _113848) ^ [_114079, _114081] : [_114081 = _114079, -(_114079 = _114081)], (230 ^ _113848) ^ [] : [complete, 233 ^ _113848 : [(234 ^ _113848) ^ [_121679, _121681] : [vertex(_121681), vertex(_121679), -(_121681 = _121679), 246 ^ _113848 : [(249 ^ _113848) ^ [] : [250 ^ _113848 : [(255 ^ _113848) ^ [] : [_121679 = head_of(245 ^ [_121679, _121681]), _121681 = tail_of(245 ^ [_121679, _121681])], (253 ^ _113848) ^ [] : [-(_121679 = tail_of(245 ^ [_121679, _121681]))], (251 ^ _113848) ^ [] : [-(_121681 = head_of(245 ^ [_121679, _121681]))]], 260 ^ _113848 : [(265 ^ _113848) ^ [] : [_121681 = head_of(245 ^ [_121679, _121681]), _121679 = tail_of(245 ^ [_121679, _121681])], (263 ^ _113848) ^ [] : [-(_121681 = tail_of(245 ^ [_121679, _121681]))], (261 ^ _113848) ^ [] : [-(_121679 = head_of(245 ^ [_121679, _121681]))]]], (247 ^ _113848) ^ [] : [-(edge(245 ^ [_121679, _121681]))]]]]], (303 ^ _113848) ^ [_123965, _123967, _123969] : [path(_123969, _123967, _123965), 306 ^ _113848 : [(309 ^ _113848) ^ [] : [-(vertex(_123967))], (312 ^ _113848) ^ [] : [-(edge(310 ^ [_123965, _123967, _123969]))], (314 ^ _113848) ^ [] : [-(_123969 = tail_of(310 ^ [_123965, _123967, _123969]))], (316 ^ _113848) ^ [] : [317 ^ _113848 : [(322 ^ _113848) ^ [_124754] : [path(head_of(310 ^ [_123965, _123967, _123969]), _123967, _124754), _123965 = path_cons(310 ^ [_123965, _123967, _123969], _124754)], (320 ^ _113848) ^ [] : [-(_123965 = path_cons(310 ^ [_123965, _123967, _123969], empty))], (318 ^ _113848) ^ [] : [-(_123967 = head_of(310 ^ [_123965, _123967, _123969]))]], 328 ^ _113848 : [(333 ^ _113848) ^ [] : [_123967 = head_of(310 ^ [_123965, _123967, _123969]), _123965 = path_cons(310 ^ [_123965, _123967, _123969], empty)], (331 ^ _113848) ^ [] : [-(_123965 = path_cons(310 ^ [_123965, _123967, _123969], 327 ^ [_123965, _123967, _123969]))], (329 ^ _113848) ^ [] : [-(path(head_of(310 ^ [_123965, _123967, _123969]), _123967, 327 ^ [_123965, _123967, _123969]))]]], (307 ^ _113848) ^ [] : [-(vertex(_123969))]]], (426 ^ _113848) ^ [_128524, _128526, _128528] : [path(_128526, _128524, _128528), 429 ^ _113848 : [(430 ^ _113848) ^ [_128719, _128721] : [precedes(_128721, _128719, _128528), 433 ^ _113848 : [(438 ^ _113848) ^ [] : [448 ^ _113848 : [(453 ^ _113848) ^ [] : [sequential(_128721, _128719)], (451 ^ _113848) ^ [] : [-(precedes(447 ^ [_128524, _128526, _128528, _128719, _128721], _128719, _128528))], (449 ^ _113848) ^ [] : [-(sequential(_128721, 447 ^ [_128524, _128526, _128528, _128719, _128721]))]], 439 ^ _113848 : [(442 ^ _113848) ^ [_129162] : [sequential(_128721, _129162), precedes(_129162, _128719, _128528)], (440 ^ _113848) ^ [] : [-(sequential(_128721, _128719))]]], (436 ^ _113848) ^ [] : [-(on_path(_128719, _128528))], (434 ^ _113848) ^ [] : [-(on_path(_128721, _128528))]]]]], (76 ^ _113848) ^ [_116416, _116418, _116420, _116422] : [-(sequential(_116420, _116416)), sequential(_116422, _116418), _116422 = _116420, _116418 = _116416], (550 ^ _113848) ^ [_133025, _133027, _133029] : [path(_133029, _133027, _133025), -(number_of_in(sequential_pairs, _133025) = minus(length_of(_133025), n1))], (486 ^ _113848) ^ [_130865, _130867, _130869, _130871, _130873] : [shortest_path(_130873, _130871, _130865), precedes(_130869, _130867, _130865), 493 ^ _113848 : [(494 ^ _113848) ^ [_131158] : [tail_of(_131158) = tail_of(_130869), head_of(_131158) = head_of(_130867)], (500 ^ _113848) ^ [] : [precedes(_130867, _130869, _130865)]]], (20 ^ _113848) ^ [_114624, _114626, _114628, _114630] : [-(in_path(_114628, _114624)), in_path(_114630, _114626), _114630 = _114628, _114626 = _114624], (339 ^ _113848) ^ [_125500, _125502, _125504, _125506] : [346 ^ _113848 : [(351 ^ _113848) ^ [] : [-(in_path(tail_of(_125500), _125502))], (349 ^ _113848) ^ [] : [-(in_path(head_of(_125500), _125502))], (347 ^ _113848) ^ [] : [-(edge(_125500))]], path(_125506, _125504, _125502), on_path(_125500, _125502)], (455 ^ _113848) ^ [_129764, _129766, _129768] : [shortest_path(_129768, _129766, _129764), 458 ^ _113848 : [(463 ^ _113848) ^ [_130063] : [path(_129768, _129766, _130063), -(less_or_equal(length_of(_129764), length_of(_130063)))], (461 ^ _113848) ^ [] : [_129768 = _129766], (459 ^ _113848) ^ [] : [-(path(_129768, _129766, _129764))]]], (353 ^ _113848) ^ [_126012, _126014, _126016, _126018] : [path(_126018, _126016, _126014), in_path(_126012, _126014), 360 ^ _113848 : [(366 ^ _113848) ^ [] : [-(_126012 = head_of(362 ^ [_126012, _126014, _126016, _126018])), -(_126012 = tail_of(362 ^ [_126012, _126014, _126016, _126018]))], (364 ^ _113848) ^ [] : [-(on_path(362 ^ [_126012, _126014, _126016, _126018], _126014))], (361 ^ _113848) ^ [] : [-(vertex(_126012))]]], (384 ^ _113848) ^ [_127122, _127124] : [-(sequential(_127124, _127122)), edge(_127124), edge(_127122), -(_127124 = _127122), head_of(_127124) = tail_of(_127122)], (178 ^ _113848) ^ [_119789, _119791, _119793, _119795] : [-(minus(_119795, _119791) = minus(_119793, _119789)), _119795 = _119793, _119791 = _119789], (10 ^ _113848) ^ [_114283, _114285, _114287] : [-(_114287 = _114283), _114287 = _114285, _114285 = _114283], (210 ^ _113848) ^ [_120895, _120897] : [_120897 = _120895, -(tail_of(_120897) = tail_of(_120895))], (44 ^ _113848) ^ [_115391, _115393, _115395, _115397, _115399, _115401] : [-(path(_115399, _115395, _115391)), path(_115401, _115397, _115393), _115401 = _115399, _115397 = _115395, _115393 = _115391], (271 ^ _113848) ^ [_122887, _122889, _122891] : [-(path(_122891, _122889, _122887)), vertex(_122891), vertex(_122889), 280 ^ _113848 : [(281 ^ _113848) ^ [_123197] : [edge(_123197), _122891 = tail_of(_123197), 288 ^ _113848 : [(295 ^ _113848) ^ [_123631] : [path(head_of(_123197), _122889, _123631), _122887 = path_cons(_123197, _123631)], (289 ^ _113848) ^ [] : [_122889 = head_of(_123197), _122887 = path_cons(_123197, empty)]]]]], (34 ^ _113848) ^ [_115040, _115042] : [-(vertex(_115040)), _115042 = _115040, vertex(_115042)], (222 ^ _113848) ^ [_121338] : [edge(_121338), 225 ^ _113848 : [(228 ^ _113848) ^ [] : [-(vertex(tail_of(_121338)))], (226 ^ _113848) ^ [] : [-(vertex(head_of(_121338)))]]], (216 ^ _113848) ^ [_121141] : [edge(_121141), head_of(_121141) = tail_of(_121141)], (402 ^ _113848) ^ [_127622, _127624, _127626] : [path(_127624, _127622, _127626), 405 ^ _113848 : [(406 ^ _113848) ^ [_127815, _127817] : [-(precedes(_127817, _127815, _127626)), on_path(_127817, _127626), on_path(_127815, _127626), 415 ^ _113848 : [(418 ^ _113848) ^ [_128192] : [sequential(_127817, _128192), precedes(_128192, _127815, _127626)], (416 ^ _113848) ^ [] : [sequential(_127817, _127815)]]]]], (469 ^ _113848) ^ [_130262, _130264, _130266] : [-(shortest_path(_130266, _130264, _130262)), path(_130266, _130264, _130262), -(_130266 = _130264), 479 ^ _113848 : [(482 ^ _113848) ^ [] : [less_or_equal(length_of(_130262), length_of(478 ^ [_130262, _130264, _130266]))], (480 ^ _113848) ^ [] : [-(path(_130266, _130264, 478 ^ [_130262, _130264, _130266]))]]], (502 ^ _113848) ^ [_131545, _131547, _131549] : [triangle(_131549, _131547, _131545), 505 ^ _113848 : [(514 ^ _113848) ^ [] : [-(sequential(_131547, _131545))], (512 ^ _113848) ^ [] : [-(sequential(_131549, _131547))], (516 ^ _113848) ^ [] : [-(sequential(_131545, _131549))], (506 ^ _113848) ^ [] : [-(edge(_131549))], (508 ^ _113848) ^ [] : [-(edge(_131547))], (510 ^ _113848) ^ [] : [-(edge(_131545))]]], (518 ^ _113848) ^ [_132090, _132092, _132094] : [-(triangle(_132094, _132092, _132090)), edge(_132094), edge(_132092), edge(_132090), sequential(_132094, _132092), sequential(_132092, _132090), sequential(_132090, _132094)], (90 ^ _113848) ^ [_116888, _116890, _116892, _116894, _116896, _116898] : [-(triangle(_116896, _116892, _116888)), triangle(_116898, _116894, _116890), _116898 = _116896, _116894 = _116892, _116890 = _116888], (188 ^ _113848) ^ [_120120, _120122] : [_120122 = _120120, -(length_of(_120122) = length_of(_120120))], (2 ^ _113848) ^ [_113972] : [-(_113972 = _113972)], (556 ^ _113848) ^ [_133273, _133275, _133277] : [-(number_of_in(sequential_pairs, _133277) = number_of_in(triangles, _133277)), path(_133275, _133273, _133277), 563 ^ _113848 : [(570 ^ _113848) ^ [_133893] : [triangle(561 ^ [_133273, _133275, _133277], 562 ^ [_133273, _133275, _133277], _133893)], (564 ^ _113848) ^ [] : [-(on_path(561 ^ [_133273, _133275, _133277], _133277))], (568 ^ _113848) ^ [] : [-(sequential(561 ^ [_133273, _133275, _133277], 562 ^ [_133273, _133275, _133277]))], (566 ^ _113848) ^ [] : [-(on_path(562 ^ [_133273, _133275, _133277], _133277))]]], (168 ^ _113848) ^ [_119430, _119432, _119434, _119436] : [-(path_cons(_119436, _119432) = path_cons(_119434, _119430)), _119436 = _119434, _119432 = _119430], (158 ^ _113848) ^ [_119083, _119085] : [-(edge(_119083)), _119085 = _119083, edge(_119085)]], input).
% 219.90/211.86  ncf('1',plain,[edge(579 ^ []), tail_of(579 ^ []) = head_of(580 ^ []), head_of(579 ^ []) = tail_of(579 ^ [])],start(587 ^ 0,bind([[_134821], [579 ^ []]]))).
% 219.90/211.86  ncf('1.1',plain,[-(edge(579 ^ [])), sequential(579 ^ [], 580 ^ [])],extension(372 ^ 1,bind([[_126732, _126734], [580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.1.1',plain,[-(sequential(579 ^ [], 580 ^ [])), 449 : -(sequential(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []])), 438 : precedes(579 ^ [], 580 ^ [], 581 ^ []), 430 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(426 ^ 2,bind([[_128524, _128526, _128528, _128719, _128721], [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.1.1.1',plain,[sequential(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []]), 376 : -(edge(579 ^ []))],extension(372 ^ 9,bind([[_126732, _126734], [447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []], 579 ^ []]]))).
% 219.90/211.86  ncf('1.1.1.1.1',plain,[edge(579 ^ [])],reduction('1')).
% 219.90/211.86  ncf('1.1.1.2',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 5)).
% 219.90/211.86  ncf('1.1.1.3',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 3,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.1.1.3.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 4)).
% 219.90/211.86  ncf('1.2',plain,[-(tail_of(579 ^ []) = head_of(580 ^ [])), head_of(580 ^ []) = tail_of(579 ^ [])],extension(4 ^ 1,bind([[_114079, _114081], [tail_of(579 ^ []), head_of(580 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1',plain,[-(head_of(580 ^ []) = tail_of(579 ^ [])), 234 : vertex(head_of(580 ^ [])), 234 : vertex(tail_of(579 ^ [])), 251 : -(head_of(580 ^ []) = head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])])), 263 : -(head_of(580 ^ []) = tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])])), 234 : complete],extension(230 ^ 2,bind([[_121679, _121681], [tail_of(579 ^ []), head_of(580 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1.1',plain,[-(vertex(head_of(580 ^ []))), path(577 ^ [], 578 ^ [], 581 ^ []), in_path(head_of(580 ^ []), 581 ^ [])],extension(353 ^ 5,bind([[_126012, _126014, _126016, _126018], [head_of(580 ^ []), 581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.1',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 6,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 7)).
% 219.90/211.86  ncf('1.2.1.1.2',plain,[-(in_path(head_of(580 ^ []), 581 ^ [])), path(577 ^ [], 578 ^ [], 581 ^ []), on_path(580 ^ [], 581 ^ [])],extension(339 ^ 6,bind([[_125500, _125502, _125504, _125506], [580 ^ [], 581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.2.1',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 7,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.2.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 8)).
% 219.90/211.86  ncf('1.2.1.1.2.2',plain,[-(on_path(580 ^ [], 581 ^ [])), 430 : precedes(579 ^ [], 580 ^ [], 581 ^ []), 430 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(426 ^ 7,bind([[_128524, _128526, _128528, _128719, _128721], [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.2.2.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 10)).
% 219.90/211.86  ncf('1.2.1.1.2.2.2',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 8,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.1.2.2.2.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 9)).
% 219.90/211.86  ncf('1.2.1.2',plain,[-(vertex(tail_of(579 ^ []))), path(577 ^ [], 578 ^ [], 581 ^ []), in_path(tail_of(579 ^ []), 581 ^ [])],extension(353 ^ 5,bind([[_126012, _126014, _126016, _126018], [tail_of(579 ^ []), 581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.1',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 6,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 7)).
% 219.90/211.86  ncf('1.2.1.2.2',plain,[-(in_path(tail_of(579 ^ []), 581 ^ [])), path(577 ^ [], 578 ^ [], 581 ^ []), on_path(579 ^ [], 581 ^ [])],extension(339 ^ 6,bind([[_125500, _125502, _125504, _125506], [579 ^ [], 581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.2.1',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 7,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.2.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 8)).
% 219.90/211.86  ncf('1.2.1.2.2.2',plain,[-(on_path(579 ^ [], 581 ^ [])), 430 : precedes(579 ^ [], 580 ^ [], 581 ^ []), 430 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(426 ^ 7,bind([[_128524, _128526, _128528, _128719, _128721], [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.2.2.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 10)).
% 219.90/211.86  ncf('1.2.1.2.2.2.2',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 8,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.2.1.2.2.2.2.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 9)).
% 219.90/211.86  ncf('1.2.1.3',plain,[head_of(580 ^ []) = head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), -(head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = head_of(580 ^ []))],extension(4 ^ 9,bind([[_114079, _114081], [head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), head_of(580 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1.3.1',plain,[head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = head_of(580 ^ []), 494 : tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = tail_of(579 ^ []), 494 : shortest_path(577 ^ [], 578 ^ [], 581 ^ []), 494 : precedes(579 ^ [], 580 ^ [], 581 ^ [])],extension(486 ^ 10,bind([[_130865, _130867, _130869, _130871, _130873, _131158], [581 ^ [], 580 ^ [], 579 ^ [], 578 ^ [], 577 ^ [], 245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]]]))).
% 219.90/211.86  ncf('1.2.1.3.1.1',plain,[-(tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = tail_of(579 ^ [])), tail_of(579 ^ []) = tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])])],extension(4 ^ 13,bind([[_114079, _114081], [tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), tail_of(579 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1.3.1.1.1',plain,[-(tail_of(579 ^ []) = tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]))],extension(253 ^ 14)).
% 219.90/211.86  ncf('1.2.1.3.1.2',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 11)).
% 219.90/211.86  ncf('1.2.1.3.1.3',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 11)).
% 219.90/211.86  ncf('1.2.1.4',plain,[head_of(580 ^ []) = tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), -(tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = head_of(580 ^ []))],extension(4 ^ 9,bind([[_114079, _114081], [tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), head_of(580 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1.4.1',plain,[tail_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = head_of(580 ^ []), edge(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = tail_of(579 ^ [])],extension(587 ^ 10,bind([[_134821], [245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]]]))).
% 219.90/211.86  ncf('1.2.1.4.1.1',plain,[-(edge(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]))],extension(247 ^ 11)).
% 219.90/211.86  ncf('1.2.1.4.1.2',plain,[-(head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]) = tail_of(579 ^ [])), tail_of(579 ^ []) = head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])])],extension(4 ^ 11,bind([[_114079, _114081], [head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]), tail_of(579 ^ [])]]))).
% 219.90/211.86  ncf('1.2.1.4.1.2.1',plain,[-(tail_of(579 ^ []) = head_of(245 ^ [tail_of(579 ^ []), head_of(580 ^ [])]))],extension(261 ^ 12)).
% 219.90/211.86  ncf('1.2.1.5',plain,[-(complete)],extension(576 ^ 3)).
% 219.90/211.86  ncf('1.3',plain,[-(head_of(579 ^ []) = tail_of(579 ^ [])), sequential(579 ^ [], 579 ^ [])],extension(372 ^ 1,bind([[_126732, _126734], [579 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1',plain,[-(sequential(579 ^ [], 579 ^ [])), 451 : -(precedes(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 579 ^ [], 581 ^ [])), 438 : precedes(579 ^ [], 579 ^ [], 581 ^ []), 430 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(426 ^ 2,bind([[_128524, _128526, _128528, _128719, _128721], [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1',plain,[precedes(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 579 ^ [], 581 ^ []), shortest_path(577 ^ [], 578 ^ [], 581 ^ []), 500 : precedes(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 581 ^ [])],extension(486 ^ 9,bind([[_130865, _130867, _130869, _130871, _130873], [581 ^ [], 579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 10)).
% 219.90/211.86  ncf('1.3.1.1.2',plain,[-(precedes(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 581 ^ [])), 406 : on_path(579 ^ [], 581 ^ []), 406 : on_path(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 581 ^ []), 416 : sequential(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []]), 406 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(402 ^ 12,bind([[_127622, _127624, _127626, _127815, _127817], [578 ^ [], 577 ^ [], 581 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.2.1',plain,[-(on_path(579 ^ [], 581 ^ [])), on_path(579 ^ [], 581 ^ []), 579 ^ [] = 579 ^ [], 581 ^ [] = 581 ^ []],extension(62 ^ 15,bind([[_115972, _115974, _115976, _115978], [581 ^ [], 581 ^ [], 579 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.2.1.1',plain,[-(on_path(579 ^ [], 581 ^ []))],extension(436 ^ 16)).
% 219.90/211.86  ncf('1.3.1.1.2.1.2',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 16,bind([[_113972], [579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.2.1.3',plain,[-(581 ^ [] = 581 ^ [])],extension(2 ^ 16,bind([[_113972], [581 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.2.2',plain,[-(on_path(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 581 ^ [])), precedes(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 579 ^ [], 581 ^ [])],extension(430 ^ 15,bind([[_128719, _128721], [579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []]]]))).
% 219.90/211.86  ncf('1.3.1.1.2.2.1',plain,[-(precedes(447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []], 579 ^ [], 581 ^ []))],reduction('1.3.1')).
% 219.90/211.86  ncf('1.3.1.1.2.3',plain,[-(sequential(579 ^ [], 447 ^ [578 ^ [], 577 ^ [], 581 ^ [], 579 ^ [], 579 ^ []]))],extension(449 ^ 17)).
% 219.90/211.86  ncf('1.3.1.1.2.4',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 13,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.1.2.4.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 14)).
% 219.90/211.86  ncf('1.3.1.2',plain,[-(precedes(579 ^ [], 579 ^ [], 581 ^ [])), precedes(579 ^ [], 580 ^ [], 581 ^ []), 579 ^ [] = 579 ^ [], 580 ^ [] = 579 ^ [], 581 ^ [] = 581 ^ []],extension(140 ^ 5,bind([[_118550, _118552, _118554, _118556, _118558, _118560], [581 ^ [], 581 ^ [], 579 ^ [], 580 ^ [], 579 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 6)).
% 219.90/211.86  ncf('1.3.1.2.2',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 6,bind([[_113972], [579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3',plain,[-(580 ^ [] = 579 ^ []), -(sequential(580 ^ [], 579 ^ [])), edge(580 ^ []), edge(579 ^ []), head_of(580 ^ []) = tail_of(579 ^ [])],extension(384 ^ 6,bind([[_127122, _127124], [579 ^ [], 580 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.1',plain,[sequential(580 ^ [], 579 ^ []), 418 : precedes(579 ^ [], 580 ^ [], 581 ^ []), 418 : -(precedes(580 ^ [], 580 ^ [], 581 ^ [])), 418 : on_path(580 ^ [], 581 ^ []), 418 : on_path(580 ^ [], 581 ^ []), 406 : path(577 ^ [], 578 ^ [], 581 ^ [])],extension(402 ^ 7,bind([[_127622, _127624, _127626, _127815, _127817, _128192], [578 ^ [], 577 ^ [], 581 ^ [], 580 ^ [], 580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.1.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 12)).
% 219.90/211.86  ncf('1.3.1.2.3.1.2',plain,[precedes(580 ^ [], 580 ^ [], 581 ^ []), shortest_path(577 ^ [], 578 ^ [], 581 ^ []), 500 : precedes(580 ^ [], 580 ^ [], 581 ^ [])],extension(486 ^ 10,bind([[_130865, _130867, _130869, _130871, _130873], [581 ^ [], 580 ^ [], 580 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.1.2.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 11)).
% 219.90/211.86  ncf('1.3.1.2.3.1.2.2',plain,[-(precedes(580 ^ [], 580 ^ [], 581 ^ []))],reduction('1.3.1.2.3.1')).
% 219.90/211.86  ncf('1.3.1.2.3.1.3',plain,[-(on_path(580 ^ [], 581 ^ [])), precedes(579 ^ [], 580 ^ [], 581 ^ [])],extension(430 ^ 10,bind([[_128719, _128721], [580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.1.3.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 11)).
% 219.90/211.86  ncf('1.3.1.2.3.1.4',plain,[-(on_path(580 ^ [], 581 ^ []))],lemmata('[3, 2, 1, 3, 1].x')).
% 219.90/211.86  ncf('1.3.1.2.3.1.5',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 8,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.1.5.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 9)).
% 219.90/211.86  ncf('1.3.1.2.3.2',plain,[-(edge(580 ^ [])), path(577 ^ [], 578 ^ [], 581 ^ []), on_path(580 ^ [], 581 ^ [])],extension(339 ^ 7,bind([[_125500, _125502, _125504, _125506], [580 ^ [], 581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.2.1',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 8,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.2.1.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 9)).
% 219.90/211.86  ncf('1.3.1.2.3.2.2',plain,[-(on_path(580 ^ [], 581 ^ [])), precedes(579 ^ [], 580 ^ [], 581 ^ [])],extension(430 ^ 8,bind([[_128719, _128721], [580 ^ [], 579 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.2.3.2.2.1',plain,[-(precedes(579 ^ [], 580 ^ [], 581 ^ []))],extension(585 ^ 9)).
% 219.90/211.86  ncf('1.3.1.2.3.3',plain,[-(edge(579 ^ []))],lemmata('x')).
% 219.90/211.86  ncf('1.3.1.2.3.4',plain,[-(head_of(580 ^ []) = tail_of(579 ^ [])), tail_of(579 ^ []) = head_of(580 ^ [])],extension(4 ^ 7,bind([[_114079, _114081], [head_of(580 ^ []), tail_of(579 ^ [])]]))).
% 219.90/211.86  ncf('1.3.1.2.3.4.1',plain,[-(tail_of(579 ^ []) = head_of(580 ^ []))],lemmata('x')).
% 219.90/211.86  ncf('1.3.1.2.4',plain,[-(581 ^ [] = 581 ^ [])],extension(2 ^ 6,bind([[_113972], [581 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.3',plain,[-(path(577 ^ [], 578 ^ [], 581 ^ [])), shortest_path(577 ^ [], 578 ^ [], 581 ^ [])],extension(455 ^ 3,bind([[_129764, _129766, _129768], [581 ^ [], 578 ^ [], 577 ^ []]]))).
% 219.90/211.86  ncf('1.3.1.3.1',plain,[-(shortest_path(577 ^ [], 578 ^ [], 581 ^ []))],extension(583 ^ 4)).
% 219.90/211.86  %-----------------------------------------------------
% 219.90/211.86  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------