%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.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 48.90s 47.85s
% Output   : Proof 48.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n031.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 21:01:40 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 48.90/47.85  
% 48.90/47.85  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 48.90/47.85  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.90/47.85  %-----------------------------------------------------
% 48.90/47.85  ncf(matrix, plain, [(585 ^ _128411) ^ [] : [587 ^ _128411 : [(590 ^ _128411) ^ [] : [-(head_of(586 ^ []) = head_of(578 ^ []))], (588 ^ _128411) ^ [] : [-(tail_of(586 ^ []) = tail_of(577 ^ []))]], -(head_of(578 ^ []) = tail_of(577 ^ [])), -(head_of(578 ^ []) = head_of(577 ^ []))], (583 ^ _128411) ^ [] : [-(precedes(577 ^ [], 578 ^ [], 579 ^ []))], (581 ^ _128411) ^ [] : [-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))], !, (150 ^ _107578) ^ [_112555, _112557, _112559, _112561, _112563, _112565] : [-(precedes(_112563, _112559, _112555)), precedes(_112565, _112561, _112557), _112565 = _112563, _112561 = _112559, _112557 = _112555], (353 ^ _107578) ^ [_119742, _119744, _119746, _119748] : [path(_119748, _119746, _119744), in_path(_119742, _119744), 360 ^ _107578 : [(366 ^ _107578) ^ [] : [-(_119742 = head_of(362 ^ [_119742, _119744, _119746, _119748])), -(_119742 = tail_of(362 ^ [_119742, _119744, _119746, _119748]))], (364 ^ _107578) ^ [] : [-(on_path(362 ^ [_119742, _119744, _119746, _119748], _119744))], (361 ^ _107578) ^ [] : [-(vertex(_119742))]]], (544 ^ _107578) ^ [_126513, _126515, _126517] : [path(_126517, _126515, _126513), -(length_of(_126513) = number_of_in(edges, _126513))], (54 ^ _107578) ^ [_109416, _109418, _109420, _109422, _109424, _109426] : [-(path(_109424, _109420, _109416)), path(_109426, _109422, _109418), _109426 = _109424, _109422 = _109420, _109418 = _109416], (118 ^ _107578) ^ [_111494, _111496, _111498, _111500] : [-(less_or_equal(_111498, _111494)), less_or_equal(_111500, _111496), _111500 = _111498, _111496 = _111494], (372 ^ _107578) ^ [_120462, _120464] : [sequential(_120464, _120462), 375 ^ _107578 : [(378 ^ _107578) ^ [] : [-(edge(_120462))], (380 ^ _107578) ^ [] : [_120464 = _120462], (382 ^ _107578) ^ [] : [-(head_of(_120464) = tail_of(_120462))], (376 ^ _107578) ^ [] : [-(edge(_120464))]]], (34 ^ _107578) ^ [_108770, _108772] : [-(vertex(_108770)), _108772 = _108770, vertex(_108772)], (44 ^ _107578) ^ [_109065, _109067] : [-(edge(_109065)), _109067 = _109065, edge(_109067)], (402 ^ _107578) ^ [_121352, _121354, _121356] : [path(_121354, _121352, _121356), 405 ^ _107578 : [(406 ^ _107578) ^ [_121545, _121547] : [-(precedes(_121547, _121545, _121356)), on_path(_121547, _121356), on_path(_121545, _121356), 415 ^ _107578 : [(418 ^ _107578) ^ [_121922] : [sequential(_121547, _121922), precedes(_121922, _121545, _121356)], (416 ^ _107578) ^ [] : [sequential(_121547, _121545)]]]]], (469 ^ _107578) ^ [_123992, _123994, _123996] : [-(shortest_path(_123996, _123994, _123992)), path(_123996, _123994, _123992), -(_123996 = _123994), 479 ^ _107578 : [(482 ^ _107578) ^ [] : [less_or_equal(length_of(_123992), length_of(478 ^ [_123992, _123994, _123996]))], (480 ^ _107578) ^ [] : [-(path(_123996, _123994, 478 ^ [_123992, _123994, _123996]))]]], (455 ^ _107578) ^ [_123494, _123496, _123498] : [shortest_path(_123498, _123496, _123494), 458 ^ _107578 : [(463 ^ _107578) ^ [_123793] : [path(_123498, _123496, _123793), -(less_or_equal(length_of(_123494), length_of(_123793)))], (461 ^ _107578) ^ [] : [_123498 = _123496], (459 ^ _107578) ^ [] : [-(path(_123498, _123496, _123494))]]], (210 ^ _107578) ^ [_114625, _114627] : [_114627 = _114625, -(head_of(_114627) = head_of(_114625))], (271 ^ _107578) ^ [_116617, _116619, _116621] : [-(path(_116621, _116619, _116617)), vertex(_116621), vertex(_116619), 280 ^ _107578 : [(281 ^ _107578) ^ [_116927] : [edge(_116927), _116621 = tail_of(_116927), 288 ^ _107578 : [(295 ^ _107578) ^ [_117361] : [path(head_of(_116927), _116619, _117361), _116617 = path_cons(_116927, _117361)], (289 ^ _107578) ^ [] : [_116619 = head_of(_116927), _116617 = path_cons(_116927, empty)]]]]], (10 ^ _107578) ^ [_108013, _108015, _108017] : [-(_108017 = _108013), _108017 = _108015, _108015 = _108013], (204 ^ _107578) ^ [_114427, _114429] : [_114429 = _114427, -(tail_of(_114429) = tail_of(_114427))], (556 ^ _107578) ^ [_127003, _127005, _127007] : [-(number_of_in(sequential_pairs, _127007) = number_of_in(triangles, _127007)), path(_127005, _127003, _127007), 563 ^ _107578 : [(566 ^ _107578) ^ [] : [-(on_path(562 ^ [_127003, _127005, _127007], _127007))], (568 ^ _107578) ^ [] : [-(sequential(561 ^ [_127003, _127005, _127007], 562 ^ [_127003, _127005, _127007]))], (570 ^ _107578) ^ [_127623] : [triangle(561 ^ [_127003, _127005, _127007], 562 ^ [_127003, _127005, _127007], _127623)], (564 ^ _107578) ^ [] : [-(on_path(561 ^ [_127003, _127005, _127007], _127007))]]], (230 ^ _107578) ^ [] : [complete, 233 ^ _107578 : [(234 ^ _107578) ^ [_115409, _115411] : [vertex(_115411), vertex(_115409), -(_115411 = _115409), 246 ^ _107578 : [(249 ^ _107578) ^ [] : [250 ^ _107578 : [(255 ^ _107578) ^ [] : [_115409 = head_of(245 ^ [_115409, _115411]), _115411 = tail_of(245 ^ [_115409, _115411])], (253 ^ _107578) ^ [] : [-(_115409 = tail_of(245 ^ [_115409, _115411]))], (251 ^ _107578) ^ [] : [-(_115411 = head_of(245 ^ [_115409, _115411]))]], 260 ^ _107578 : [(265 ^ _107578) ^ [] : [_115411 = head_of(245 ^ [_115409, _115411]), _115409 = tail_of(245 ^ [_115409, _115411])], (263 ^ _107578) ^ [] : [-(_115411 = tail_of(245 ^ [_115409, _115411]))], (261 ^ _107578) ^ [] : [-(_115409 = head_of(245 ^ [_115409, _115411]))]]], (247 ^ _107578) ^ [] : [-(edge(245 ^ [_115409, _115411]))]]]]], (426 ^ _107578) ^ [_122254, _122256, _122258] : [path(_122256, _122254, _122258), 429 ^ _107578 : [(430 ^ _107578) ^ [_122449, _122451] : [precedes(_122451, _122449, _122258), 433 ^ _107578 : [(438 ^ _107578) ^ [] : [448 ^ _107578 : [(453 ^ _107578) ^ [] : [sequential(_122451, _122449)], (451 ^ _107578) ^ [] : [-(precedes(447 ^ [_122254, _122256, _122258, _122449, _122451], _122449, _122258))], (449 ^ _107578) ^ [] : [-(sequential(_122451, 447 ^ [_122254, _122256, _122258, _122449, _122451]))]], 439 ^ _107578 : [(442 ^ _107578) ^ [_122892] : [sequential(_122451, _122892), precedes(_122892, _122449, _122258)], (440 ^ _107578) ^ [] : [-(sequential(_122451, _122449))]]], (436 ^ _107578) ^ [] : [-(on_path(_122449, _122258))], (434 ^ _107578) ^ [] : [-(on_path(_122451, _122258))]]]]], (384 ^ _107578) ^ [_120852, _120854] : [-(sequential(_120854, _120852)), edge(_120854), edge(_120852), -(_120854 = _120852), head_of(_120854) = tail_of(_120852)], (100 ^ _107578) ^ [_110913, _110915, _110917, _110919, _110921, _110923] : [-(triangle(_110921, _110917, _110913)), triangle(_110923, _110919, _110915), _110923 = _110921, _110919 = _110917, _110915 = _110913], (550 ^ _107578) ^ [_126755, _126757, _126759] : [path(_126759, _126757, _126755), -(number_of_in(sequential_pairs, _126755) = minus(length_of(_126755), n1))], (86 ^ _107578) ^ [_110441, _110443, _110445, _110447] : [-(sequential(_110445, _110441)), sequential(_110447, _110443), _110447 = _110445, _110443 = _110441], (178 ^ _107578) ^ [_113519, _113521, _113523, _113525] : [-(minus(_113525, _113521) = minus(_113523, _113519)), _113525 = _113523, _113521 = _113519], (188 ^ _107578) ^ [_113850, _113852] : [_113852 = _113850, -(length_of(_113852) = length_of(_113850))], (222 ^ _107578) ^ [_115068] : [edge(_115068), 225 ^ _107578 : [(228 ^ _107578) ^ [] : [-(vertex(tail_of(_115068)))], (226 ^ _107578) ^ [] : [-(vertex(head_of(_115068)))]]], (216 ^ _107578) ^ [_114871] : [edge(_114871), head_of(_114871) = tail_of(_114871)], (4 ^ _107578) ^ [_107809, _107811] : [_107811 = _107809, -(_107809 = _107811)], (168 ^ _107578) ^ [_113160, _113162, _113164, _113166] : [-(path_cons(_113166, _113162) = path_cons(_113164, _113160)), _113166 = _113164, _113162 = _113160], (303 ^ _107578) ^ [_117695, _117697, _117699] : [path(_117699, _117697, _117695), 306 ^ _107578 : [(307 ^ _107578) ^ [] : [-(vertex(_117699))], (312 ^ _107578) ^ [] : [-(edge(310 ^ [_117695, _117697, _117699]))], (316 ^ _107578) ^ [] : [317 ^ _107578 : [(322 ^ _107578) ^ [_118484] : [path(head_of(310 ^ [_117695, _117697, _117699]), _117697, _118484), _117695 = path_cons(310 ^ [_117695, _117697, _117699], _118484)], (320 ^ _107578) ^ [] : [-(_117695 = path_cons(310 ^ [_117695, _117697, _117699], empty))], (318 ^ _107578) ^ [] : [-(_117697 = head_of(310 ^ [_117695, _117697, _117699]))]], 328 ^ _107578 : [(333 ^ _107578) ^ [] : [_117697 = head_of(310 ^ [_117695, _117697, _117699]), _117695 = path_cons(310 ^ [_117695, _117697, _117699], empty)], (331 ^ _107578) ^ [] : [-(_117695 = path_cons(310 ^ [_117695, _117697, _117699], 327 ^ [_117695, _117697, _117699]))], (329 ^ _107578) ^ [] : [-(path(head_of(310 ^ [_117695, _117697, _117699]), _117697, 327 ^ [_117695, _117697, _117699]))]]], (314 ^ _107578) ^ [] : [-(_117699 = tail_of(310 ^ [_117695, _117697, _117699]))], (309 ^ _107578) ^ [] : [-(vertex(_117697))]]], (518 ^ _107578) ^ [_125820, _125822, _125824] : [-(triangle(_125824, _125822, _125820)), edge(_125824), edge(_125822), edge(_125820), sequential(_125824, _125822), sequential(_125822, _125820), sequential(_125820, _125824)], (20 ^ _107578) ^ [_108354, _108356, _108358, _108360] : [-(in_path(_108358, _108354)), in_path(_108360, _108356), _108360 = _108358, _108356 = _108354], (2 ^ _107578) ^ [_107702] : [-(_107702 = _107702)], (502 ^ _107578) ^ [_125275, _125277, _125279] : [triangle(_125279, _125277, _125275), 505 ^ _107578 : [(508 ^ _107578) ^ [] : [-(edge(_125277))], (506 ^ _107578) ^ [] : [-(edge(_125279))], (516 ^ _107578) ^ [] : [-(sequential(_125275, _125279))], (512 ^ _107578) ^ [] : [-(sequential(_125279, _125277))], (514 ^ _107578) ^ [] : [-(sequential(_125277, _125275))], (510 ^ _107578) ^ [] : [-(edge(_125275))]]], (574 ^ _107578) ^ [_127789, _127791] : [-(less_or_equal(number_of_in(_127791, _127789), number_of_in(_127791, graph)))], (72 ^ _107578) ^ [_109997, _109999, _110001, _110003] : [-(on_path(_110001, _109997)), on_path(_110003, _109999), _110003 = _110001, _109999 = _109997], (486 ^ _107578) ^ [_124595, _124597, _124599, _124601, _124603] : [shortest_path(_124603, _124601, _124595), precedes(_124599, _124597, _124595), 493 ^ _107578 : [(494 ^ _107578) ^ [_124888] : [tail_of(_124888) = tail_of(_124599), head_of(_124888) = head_of(_124597)], (500 ^ _107578) ^ [] : [precedes(_124597, _124599, _124595)]]], (132 ^ _107578) ^ [_111966, _111968, _111970, _111972, _111974, _111976] : [-(shortest_path(_111974, _111970, _111966)), shortest_path(_111976, _111972, _111968), _111976 = _111974, _111972 = _111970, _111968 = _111966], (194 ^ _107578) ^ [_114096, _114098, _114100, _114102] : [-(number_of_in(_114102, _114098) = number_of_in(_114100, _114096)), _114102 = _114100, _114098 = _114096], (339 ^ _107578) ^ [_119230, _119232, _119234, _119236] : [346 ^ _107578 : [(351 ^ _107578) ^ [] : [-(in_path(tail_of(_119230), _119232))], (349 ^ _107578) ^ [] : [-(in_path(head_of(_119230), _119232))], (347 ^ _107578) ^ [] : [-(edge(_119230))]], path(_119236, _119234, _119232), on_path(_119230, _119232)]], input).
% 48.90/47.85  ncf('1',plain,[590 : -(head_of(586 ^ []) = head_of(578 ^ [])), 590 : -(head_of(578 ^ []) = tail_of(577 ^ [])), 590 : -(head_of(578 ^ []) = head_of(577 ^ []))],start(585 ^ 0)).
% 48.90/47.85  ncf('1.1',plain,[head_of(586 ^ []) = head_of(578 ^ []), -(head_of(586 ^ []) = head_of(578 ^ [])), head_of(586 ^ []) = head_of(586 ^ [])],extension(10 ^ 3,bind([[_108013, _108015, _108017], [head_of(578 ^ []), head_of(586 ^ []), head_of(586 ^ [])]]))).
% 48.90/47.85  ncf('1.1.1',plain,[head_of(586 ^ []) = head_of(578 ^ []), 494 : tail_of(586 ^ []) = tail_of(577 ^ []), 494 : shortest_path(575 ^ [], 576 ^ [], 579 ^ []), 494 : precedes(577 ^ [], 578 ^ [], 579 ^ [])],extension(486 ^ 4,bind([[_124595, _124597, _124599, _124601, _124603, _124888], [579 ^ [], 578 ^ [], 577 ^ [], 576 ^ [], 575 ^ [], 586 ^ []]]))).
% 48.90/47.85  ncf('1.1.1.1',plain,[-(tail_of(586 ^ []) = tail_of(577 ^ []))],extension(588 ^ 7)).
% 48.90/47.85  ncf('1.1.1.2',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.1.1.3',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 5)).
% 48.90/47.85  ncf('1.1.2',plain,[-(head_of(586 ^ []) = head_of(586 ^ [])), 586 ^ [] = 586 ^ []],extension(210 ^ 4,bind([[_114625, _114627], [586 ^ [], 586 ^ []]]))).
% 48.90/47.85  ncf('1.1.2.1',plain,[-(586 ^ [] = 586 ^ [])],extension(2 ^ 5,bind([[_107702], [586 ^ []]]))).
% 48.90/47.85  ncf('1.2',plain,[head_of(578 ^ []) = tail_of(577 ^ []), -(sequential(578 ^ [], 577 ^ [])), edge(578 ^ []), edge(577 ^ []), -(578 ^ [] = 577 ^ [])],extension(384 ^ 1,bind([[_120852, _120854], [577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.1',plain,[sequential(578 ^ [], 577 ^ []), 418 : precedes(577 ^ [], 578 ^ [], 579 ^ []), 418 : -(precedes(578 ^ [], 578 ^ [], 579 ^ [])), 418 : on_path(578 ^ [], 579 ^ []), 418 : on_path(578 ^ [], 579 ^ []), 406 : path(575 ^ [], 576 ^ [], 579 ^ [])],extension(402 ^ 2,bind([[_121352, _121354, _121356, _121545, _121547, _121922], [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.1',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 7)).
% 48.90/47.85  ncf('1.2.1.2',plain,[precedes(578 ^ [], 578 ^ [], 579 ^ []), -(precedes(578 ^ [], 578 ^ [], 579 ^ [])), 578 ^ [] = 578 ^ [], 578 ^ [] = 578 ^ [], 579 ^ [] = 579 ^ []],extension(150 ^ 5,bind([[_112555, _112557, _112559, _112561, _112563, _112565], [579 ^ [], 579 ^ [], 578 ^ [], 578 ^ [], 578 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.2.1',plain,[precedes(578 ^ [], 578 ^ [], 579 ^ []), shortest_path(575 ^ [], 576 ^ [], 579 ^ []), 500 : precedes(578 ^ [], 578 ^ [], 579 ^ [])],extension(486 ^ 6,bind([[_124595, _124597, _124599, _124601, _124603], [579 ^ [], 578 ^ [], 578 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.2.1.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 7)).
% 48.90/47.85  ncf('1.2.1.2.1.2',plain,[-(precedes(578 ^ [], 578 ^ [], 579 ^ []))],reduction('1.2.1.2')).
% 48.90/47.85  ncf('1.2.1.2.2',plain,[-(578 ^ [] = 578 ^ [])],extension(2 ^ 6,bind([[_107702], [578 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.2.3',plain,[-(578 ^ [] = 578 ^ [])],lemmata('[1, 2, 1].x')).
% 48.90/47.85  ncf('1.2.1.2.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 6,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.3',plain,[-(on_path(578 ^ [], 579 ^ [])), 430 : precedes(577 ^ [], 578 ^ [], 579 ^ []), 430 : path(575 ^ [], 576 ^ [], 579 ^ [])],extension(426 ^ 5,bind([[_122254, _122256, _122258, _122449, _122451], [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.3.1',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 8)).
% 48.90/47.85  ncf('1.2.1.3.2',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), shortest_path(575 ^ [], 576 ^ [], 579 ^ [])],extension(455 ^ 6,bind([[_123494, _123496, _123498], [579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.3.2.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 7)).
% 48.90/47.85  ncf('1.2.1.4',plain,[-(on_path(578 ^ [], 579 ^ []))],lemmata('[2, 1].x')).
% 48.90/47.85  ncf('1.2.1.5',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), path(575 ^ [], 576 ^ [], 579 ^ []), 575 ^ [] = 575 ^ [], 576 ^ [] = 576 ^ [], 579 ^ [] = 579 ^ []],extension(54 ^ 3,bind([[_109416, _109418, _109420, _109422, _109424, _109426], [579 ^ [], 579 ^ [], 576 ^ [], 576 ^ [], 575 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.5.1',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), shortest_path(575 ^ [], 576 ^ [], 579 ^ [])],extension(455 ^ 4,bind([[_123494, _123496, _123498], [579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.5.1.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.2.1.5.2',plain,[-(575 ^ [] = 575 ^ [])],extension(2 ^ 4,bind([[_107702], [575 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.5.3',plain,[-(576 ^ [] = 576 ^ [])],extension(2 ^ 4,bind([[_107702], [576 ^ []]]))).
% 48.90/47.85  ncf('1.2.1.5.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 4,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.2.2',plain,[-(edge(578 ^ [])), path(575 ^ [], 576 ^ [], 579 ^ []), on_path(578 ^ [], 579 ^ [])],extension(339 ^ 2,bind([[_119230, _119232, _119234, _119236], [578 ^ [], 579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.1',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), path(575 ^ [], 576 ^ [], 579 ^ []), 575 ^ [] = 575 ^ [], 576 ^ [] = 576 ^ [], 579 ^ [] = 579 ^ []],extension(54 ^ 3,bind([[_109416, _109418, _109420, _109422, _109424, _109426], [579 ^ [], 579 ^ [], 576 ^ [], 576 ^ [], 575 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.1.1',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), shortest_path(575 ^ [], 576 ^ [], 579 ^ [])],extension(455 ^ 4,bind([[_123494, _123496, _123498], [579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.1.1.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.2.2.1.2',plain,[-(575 ^ [] = 575 ^ [])],extension(2 ^ 4,bind([[_107702], [575 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.1.3',plain,[-(576 ^ [] = 576 ^ [])],extension(2 ^ 4,bind([[_107702], [576 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.1.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 4,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.2',plain,[-(on_path(578 ^ [], 579 ^ [])), 430 : precedes(577 ^ [], 578 ^ [], 579 ^ []), 430 : path(575 ^ [], 576 ^ [], 579 ^ [])],extension(426 ^ 3,bind([[_122254, _122256, _122258, _122449, _122451], [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.2.1',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 6)).
% 48.90/47.85  ncf('1.2.2.2.2',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), shortest_path(575 ^ [], 576 ^ [], 579 ^ [])],extension(455 ^ 4,bind([[_123494, _123496, _123498], [579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.2.2.2.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.2.3',plain,[-(edge(577 ^ [])), sequential(577 ^ [], 578 ^ [])],extension(372 ^ 2,bind([[_120462, _120464], [578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.3.1',plain,[-(sequential(577 ^ [], 578 ^ [])), 449 : -(sequential(577 ^ [], 447 ^ [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []])), 438 : precedes(577 ^ [], 578 ^ [], 579 ^ []), 430 : path(575 ^ [], 576 ^ [], 579 ^ [])],extension(426 ^ 3,bind([[_122254, _122256, _122258, _122449, _122451], [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.3.1.1',plain,[sequential(577 ^ [], 447 ^ [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []]), 376 : -(edge(577 ^ []))],extension(372 ^ 10,bind([[_120462, _120464], [447 ^ [576 ^ [], 575 ^ [], 579 ^ [], 578 ^ [], 577 ^ []], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.3.1.1.1',plain,[edge(577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.3.1.2',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 6)).
% 48.90/47.85  ncf('1.2.3.1.3',plain,[-(path(575 ^ [], 576 ^ [], 579 ^ [])), shortest_path(575 ^ [], 576 ^ [], 579 ^ [])],extension(455 ^ 4,bind([[_123494, _123496, _123498], [579 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.3.1.3.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.2.4',plain,[578 ^ [] = 577 ^ [], -(precedes(577 ^ [], 578 ^ [], 579 ^ [])), precedes(578 ^ [], 577 ^ [], 579 ^ []), 577 ^ [] = 578 ^ [], 579 ^ [] = 579 ^ []],extension(150 ^ 2,bind([[_112555, _112557, _112559, _112561, _112563, _112565], [579 ^ [], 579 ^ [], 578 ^ [], 577 ^ [], 577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.1',plain,[precedes(577 ^ [], 578 ^ [], 579 ^ []), -(precedes(578 ^ [], 578 ^ [], 579 ^ [])), 577 ^ [] = 578 ^ [], 578 ^ [] = 578 ^ [], 579 ^ [] = 579 ^ []],extension(150 ^ 3,bind([[_112555, _112557, _112559, _112561, _112563, _112565], [579 ^ [], 579 ^ [], 578 ^ [], 578 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.1.1',plain,[precedes(578 ^ [], 578 ^ [], 579 ^ []), shortest_path(575 ^ [], 576 ^ [], 579 ^ []), 500 : precedes(578 ^ [], 578 ^ [], 579 ^ [])],extension(486 ^ 4,bind([[_124595, _124597, _124599, _124601, _124603], [579 ^ [], 578 ^ [], 578 ^ [], 576 ^ [], 575 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.1.1.1',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 5)).
% 48.90/47.85  ncf('1.2.4.1.1.2',plain,[-(precedes(578 ^ [], 578 ^ [], 579 ^ []))],reduction('1.2.4.1')).
% 48.90/47.85  ncf('1.2.4.1.2',plain,[-(577 ^ [] = 578 ^ []), 578 ^ [] = 577 ^ []],extension(4 ^ 4,bind([[_107809, _107811], [577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.1.2.1',plain,[-(578 ^ [] = 577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.4.1.3',plain,[-(578 ^ [] = 578 ^ []), 578 ^ [] = 577 ^ [], 577 ^ [] = 578 ^ []],extension(10 ^ 4,bind([[_108013, _108015, _108017], [578 ^ [], 577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.1.3.1',plain,[-(578 ^ [] = 577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.4.1.3.2',plain,[-(577 ^ [] = 578 ^ [])],lemmata('[4, 2, 1].x')).
% 48.90/47.85  ncf('1.2.4.1.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 4,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.2',plain,[-(precedes(578 ^ [], 577 ^ [], 579 ^ [])), precedes(577 ^ [], 578 ^ [], 579 ^ []), 577 ^ [] = 578 ^ [], 578 ^ [] = 577 ^ [], 579 ^ [] = 579 ^ []],extension(150 ^ 3,bind([[_112555, _112557, _112559, _112561, _112563, _112565], [579 ^ [], 579 ^ [], 577 ^ [], 578 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.2.1',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 4)).
% 48.90/47.85  ncf('1.2.4.2.2',plain,[-(577 ^ [] = 578 ^ []), 578 ^ [] = 577 ^ []],extension(4 ^ 4,bind([[_107809, _107811], [577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.2.2.1',plain,[-(578 ^ [] = 577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.4.2.3',plain,[-(578 ^ [] = 577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.4.2.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 4,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.3',plain,[-(577 ^ [] = 578 ^ []), 577 ^ [] = 578 ^ [], 578 ^ [] = 578 ^ []],extension(10 ^ 3,bind([[_108013, _108015, _108017], [578 ^ [], 578 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.3.1',plain,[-(577 ^ [] = 578 ^ []), 578 ^ [] = 577 ^ []],extension(4 ^ 4,bind([[_107809, _107811], [577 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.3.1.1',plain,[-(578 ^ [] = 577 ^ [])],reduction('1.2')).
% 48.90/47.85  ncf('1.2.4.3.2',plain,[-(578 ^ [] = 578 ^ [])],extension(2 ^ 4,bind([[_107702], [578 ^ []]]))).
% 48.90/47.85  ncf('1.2.4.4',plain,[-(579 ^ [] = 579 ^ [])],extension(2 ^ 3,bind([[_107702], [579 ^ []]]))).
% 48.90/47.85  ncf('1.3',plain,[head_of(578 ^ []) = head_of(577 ^ []), -(head_of(578 ^ []) = head_of(577 ^ [])), head_of(578 ^ []) = head_of(578 ^ [])],extension(10 ^ 1,bind([[_108013, _108015, _108017], [head_of(577 ^ []), head_of(578 ^ []), head_of(578 ^ [])]]))).
% 48.90/47.85  ncf('1.3.1',plain,[head_of(578 ^ []) = head_of(577 ^ []), -(head_of(577 ^ []) = head_of(578 ^ []))],extension(4 ^ 2,bind([[_107809, _107811], [head_of(577 ^ []), head_of(578 ^ [])]]))).
% 48.90/47.85  ncf('1.3.1.1',plain,[head_of(577 ^ []) = head_of(578 ^ []), 494 : tail_of(577 ^ []) = tail_of(577 ^ []), 494 : shortest_path(575 ^ [], 576 ^ [], 579 ^ []), 494 : precedes(577 ^ [], 578 ^ [], 579 ^ [])],extension(486 ^ 3,bind([[_124595, _124597, _124599, _124601, _124603, _124888], [579 ^ [], 578 ^ [], 577 ^ [], 576 ^ [], 575 ^ [], 577 ^ []]]))).
% 48.90/47.85  ncf('1.3.1.1.1',plain,[-(tail_of(577 ^ []) = tail_of(577 ^ []))],extension(2 ^ 6,bind([[_107702], [tail_of(577 ^ [])]]))).
% 48.90/47.85  ncf('1.3.1.1.2',plain,[-(shortest_path(575 ^ [], 576 ^ [], 579 ^ []))],extension(581 ^ 4)).
% 48.90/47.85  ncf('1.3.1.1.3',plain,[-(precedes(577 ^ [], 578 ^ [], 579 ^ []))],extension(583 ^ 4)).
% 48.90/47.85  ncf('1.3.2',plain,[-(head_of(578 ^ []) = head_of(578 ^ [])), 578 ^ [] = 578 ^ []],extension(210 ^ 2,bind([[_114625, _114627], [578 ^ [], 578 ^ []]]))).
% 48.90/47.85  ncf('1.3.2.1',plain,[-(578 ^ [] = 578 ^ [])],extension(2 ^ 3,bind([[_107702], [578 ^ []]]))).
% 48.90/47.85  %-----------------------------------------------------
% 48.90/47.85  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------