%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GRA008+2 : 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 137.68s 132.89s
% Output   : Proof 137.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 20:33:31 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 137.68/132.89  
% 137.68/132.89  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 137.68/132.89  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 137.68/132.89  %-----------------------------------------------------
% 137.68/132.89  ncf(matrix, plain, [(595 ^ _106147) ^ [] : [-(complete)], (602 ^ _106147) ^ [] : [-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))], (604 ^ _106147) ^ [] : [-(precedes(598 ^ [], 599 ^ [], 600 ^ []))], (606 ^ _106147) ^ [] : [-(sequential(598 ^ [], 599 ^ []))], (608 ^ _106147) ^ [_127859] : [triangle(598 ^ [], 599 ^ [], _127859)], (168 ^ _106147) ^ [_111749, _111751, _111753, _111755] : [-(path_cons(_111755, _111751) = path_cons(_111753, _111749)), _111755 = _111753, _111751 = _111749], (178 ^ _106147) ^ [_112108, _112110, _112112, _112114] : [-(minus(_112114, _112110) = minus(_112112, _112108)), _112114 = _112112, _112110 = _112108], (188 ^ _106147) ^ [_112439, _112441] : [_112441 = _112439, -(length_of(_112441) = length_of(_112439))], (194 ^ _106147) ^ [_112685, _112687, _112689, _112691] : [-(number_of_in(_112691, _112687) = number_of_in(_112689, _112685)), _112691 = _112689, _112687 = _112685], (204 ^ _106147) ^ [_113016, _113018] : [_113018 = _113016, -(head_of(_113018) = head_of(_113016))], (210 ^ _106147) ^ [_113214, _113216] : [_113216 = _113214, -(tail_of(_113216) = tail_of(_113214))], (2 ^ _106147) ^ [_106291] : [-(_106291 = _106291)], (4 ^ _106147) ^ [_106398, _106400] : [_106400 = _106398, -(_106398 = _106400)], (10 ^ _106147) ^ [_106602, _106604, _106606] : [-(_106606 = _106602), _106606 = _106604, _106604 = _106602], (20 ^ _106147) ^ [_106943, _106945, _106947, _106949] : [-(in_path(_106947, _106943)), in_path(_106949, _106945), _106949 = _106947, _106945 = _106943], (34 ^ _106147) ^ [_107359, _107361] : [-(vertex(_107359)), _107361 = _107359, vertex(_107361)], (44 ^ _106147) ^ [_107710, _107712, _107714, _107716, _107718, _107720] : [-(path(_107718, _107714, _107710)), path(_107720, _107716, _107712), _107720 = _107718, _107716 = _107714, _107712 = _107710], (62 ^ _106147) ^ [_108291, _108293, _108295, _108297] : [-(on_path(_108295, _108291)), on_path(_108297, _108293), _108297 = _108295, _108293 = _108291], (76 ^ _106147) ^ [_108735, _108737, _108739, _108741] : [-(less_or_equal(_108739, _108735)), less_or_equal(_108741, _108737), _108741 = _108739, _108737 = _108735], (90 ^ _106147) ^ [_109151, _109153] : [-(edge(_109151)), _109153 = _109151, edge(_109153)], (100 ^ _106147) ^ [_109502, _109504, _109506, _109508, _109510, _109512] : [-(shortest_path(_109510, _109506, _109502)), shortest_path(_109512, _109508, _109504), _109512 = _109510, _109508 = _109506, _109504 = _109502], (118 ^ _106147) ^ [_110111, _110113, _110115, _110117, _110119, _110121] : [-(precedes(_110119, _110115, _110111)), precedes(_110121, _110117, _110113), _110121 = _110119, _110117 = _110115, _110113 = _110111], (136 ^ _106147) ^ [_110692, _110694, _110696, _110698] : [-(sequential(_110696, _110692)), sequential(_110698, _110694), _110698 = _110696, _110694 = _110692], (150 ^ _106147) ^ [_111144, _111146, _111148, _111150, _111152, _111154] : [-(triangle(_111152, _111148, _111144)), triangle(_111154, _111150, _111146), _111154 = _111152, _111150 = _111148, _111146 = _111144], (502 ^ _106147) ^ [_123864, _123866, _123868] : [triangle(_123868, _123866, _123864), 505 ^ _106147 : [(506 ^ _106147) ^ [] : [-(edge(_123868))], (508 ^ _106147) ^ [] : [-(edge(_123866))], (510 ^ _106147) ^ [] : [-(edge(_123864))], (512 ^ _106147) ^ [] : [-(sequential(_123868, _123866))], (514 ^ _106147) ^ [] : [-(sequential(_123866, _123864))], (516 ^ _106147) ^ [] : [-(sequential(_123864, _123868))]]], (518 ^ _106147) ^ [_124409, _124411, _124413] : [-(triangle(_124413, _124411, _124409)), edge(_124413), edge(_124411), edge(_124409), sequential(_124413, _124411), sequential(_124411, _124409), sequential(_124409, _124413)], (544 ^ _106147) ^ [_125102, _125104, _125106] : [path(_125106, _125104, _125102), -(length_of(_125102) = number_of_in(edges, _125102))], (550 ^ _106147) ^ [_125344, _125346, _125348] : [path(_125348, _125346, _125344), -(number_of_in(sequential_pairs, _125344) = minus(length_of(_125344), n1))], (556 ^ _106147) ^ [_125592, _125594, _125596] : [-(number_of_in(sequential_pairs, _125596) = number_of_in(triangles, _125596)), path(_125594, _125592, _125596), 563 ^ _106147 : [(564 ^ _106147) ^ [] : [-(on_path(561 ^ [_125592, _125594, _125596], _125596))], (566 ^ _106147) ^ [] : [-(on_path(562 ^ [_125592, _125594, _125596], _125596))], (568 ^ _106147) ^ [] : [-(sequential(561 ^ [_125592, _125594, _125596], 562 ^ [_125592, _125594, _125596]))], (570 ^ _106147) ^ [_126212] : [triangle(561 ^ [_125592, _125594, _125596], 562 ^ [_125592, _125594, _125596], _126212)]]], (574 ^ _106147) ^ [_126398, _126400] : [-(less_or_equal(number_of_in(_126400, _126398), number_of_in(_126400, graph)))], (576 ^ _106147) ^ [] : [complete, 579 ^ _106147 : [(580 ^ _106147) ^ [_126597, _126599, _126601, _126603, _126605] : [588 ^ _106147 : [(589 ^ _106147) ^ [] : [-(edge(587 ^ [_126597, _126599, _126601, _126603, _126605]))], (591 ^ _106147) ^ [] : [-(tail_of(587 ^ [_126597, _126599, _126601, _126603, _126605]) = head_of(_126599))], (593 ^ _106147) ^ [] : [-(head_of(587 ^ [_126597, _126599, _126601, _126603, _126605]) = tail_of(_126601))]], shortest_path(_126605, _126603, _126597), precedes(_126601, _126599, _126597)]]], (216 ^ _106147) ^ [_113460] : [edge(_113460), head_of(_113460) = tail_of(_113460)], (222 ^ _106147) ^ [_113657] : [edge(_113657), 225 ^ _106147 : [(226 ^ _106147) ^ [] : [-(vertex(head_of(_113657)))], (228 ^ _106147) ^ [] : [-(vertex(tail_of(_113657)))]]], (230 ^ _106147) ^ [] : [complete, 233 ^ _106147 : [(234 ^ _106147) ^ [_113998, _114000] : [vertex(_114000), vertex(_113998), -(_114000 = _113998), 246 ^ _106147 : [(247 ^ _106147) ^ [] : [-(edge(245 ^ [_113998, _114000]))], (249 ^ _106147) ^ [] : [250 ^ _106147 : [(251 ^ _106147) ^ [] : [-(_114000 = head_of(245 ^ [_113998, _114000]))], (253 ^ _106147) ^ [] : [-(_113998 = tail_of(245 ^ [_113998, _114000]))], (255 ^ _106147) ^ [] : [_113998 = head_of(245 ^ [_113998, _114000]), _114000 = tail_of(245 ^ [_113998, _114000])]], 260 ^ _106147 : [(261 ^ _106147) ^ [] : [-(_113998 = head_of(245 ^ [_113998, _114000]))], (263 ^ _106147) ^ [] : [-(_114000 = tail_of(245 ^ [_113998, _114000]))], (265 ^ _106147) ^ [] : [_114000 = head_of(245 ^ [_113998, _114000]), _113998 = tail_of(245 ^ [_113998, _114000])]]]]]]], (271 ^ _106147) ^ [_115206, _115208, _115210] : [-(path(_115210, _115208, _115206)), vertex(_115210), vertex(_115208), 280 ^ _106147 : [(281 ^ _106147) ^ [_115516] : [edge(_115516), _115210 = tail_of(_115516), 288 ^ _106147 : [(289 ^ _106147) ^ [] : [_115208 = head_of(_115516), _115206 = path_cons(_115516, empty)], (295 ^ _106147) ^ [_115950] : [path(head_of(_115516), _115208, _115950), _115206 = path_cons(_115516, _115950)]]]]], (303 ^ _106147) ^ [_116284, _116286, _116288] : [path(_116288, _116286, _116284), 306 ^ _106147 : [(307 ^ _106147) ^ [] : [-(vertex(_116288))], (309 ^ _106147) ^ [] : [-(vertex(_116286))], (312 ^ _106147) ^ [] : [-(edge(310 ^ [_116284, _116286, _116288]))], (314 ^ _106147) ^ [] : [-(_116288 = tail_of(310 ^ [_116284, _116286, _116288]))], (316 ^ _106147) ^ [] : [317 ^ _106147 : [(318 ^ _106147) ^ [] : [-(_116286 = head_of(310 ^ [_116284, _116286, _116288]))], (320 ^ _106147) ^ [] : [-(_116284 = path_cons(310 ^ [_116284, _116286, _116288], empty))], (322 ^ _106147) ^ [_117073] : [path(head_of(310 ^ [_116284, _116286, _116288]), _116286, _117073), _116284 = path_cons(310 ^ [_116284, _116286, _116288], _117073)]], 328 ^ _106147 : [(329 ^ _106147) ^ [] : [-(path(head_of(310 ^ [_116284, _116286, _116288]), _116286, 327 ^ [_116284, _116286, _116288]))], (331 ^ _106147) ^ [] : [-(_116284 = path_cons(310 ^ [_116284, _116286, _116288], 327 ^ [_116284, _116286, _116288]))], (333 ^ _106147) ^ [] : [_116286 = head_of(310 ^ [_116284, _116286, _116288]), _116284 = path_cons(310 ^ [_116284, _116286, _116288], empty)]]]]], (339 ^ _106147) ^ [_117819, _117821, _117823, _117825] : [346 ^ _106147 : [(347 ^ _106147) ^ [] : [-(edge(_117819))], (349 ^ _106147) ^ [] : [-(in_path(head_of(_117819), _117821))], (351 ^ _106147) ^ [] : [-(in_path(tail_of(_117819), _117821))]], path(_117825, _117823, _117821), on_path(_117819, _117821)], (353 ^ _106147) ^ [_118331, _118333, _118335, _118337] : [path(_118337, _118335, _118333), in_path(_118331, _118333), 360 ^ _106147 : [(361 ^ _106147) ^ [] : [-(vertex(_118331))], (364 ^ _106147) ^ [] : [-(on_path(362 ^ [_118331, _118333, _118335, _118337], _118333))], (366 ^ _106147) ^ [] : [-(_118331 = head_of(362 ^ [_118331, _118333, _118335, _118337])), -(_118331 = tail_of(362 ^ [_118331, _118333, _118335, _118337]))]]], (372 ^ _106147) ^ [_119051, _119053] : [sequential(_119053, _119051), 375 ^ _106147 : [(376 ^ _106147) ^ [] : [-(edge(_119053))], (378 ^ _106147) ^ [] : [-(edge(_119051))], (380 ^ _106147) ^ [] : [_119053 = _119051], (382 ^ _106147) ^ [] : [-(head_of(_119053) = tail_of(_119051))]]], (384 ^ _106147) ^ [_119441, _119443] : [-(sequential(_119443, _119441)), edge(_119443), edge(_119441), -(_119443 = _119441), head_of(_119443) = tail_of(_119441)], (402 ^ _106147) ^ [_119941, _119943, _119945] : [path(_119943, _119941, _119945), 405 ^ _106147 : [(406 ^ _106147) ^ [_120134, _120136] : [-(precedes(_120136, _120134, _119945)), on_path(_120136, _119945), on_path(_120134, _119945), 415 ^ _106147 : [(416 ^ _106147) ^ [] : [sequential(_120136, _120134)], (418 ^ _106147) ^ [_120511] : [sequential(_120136, _120511), precedes(_120511, _120134, _119945)]]]]], (426 ^ _106147) ^ [_120843, _120845, _120847] : [path(_120845, _120843, _120847), 429 ^ _106147 : [(430 ^ _106147) ^ [_121038, _121040] : [precedes(_121040, _121038, _120847), 433 ^ _106147 : [(434 ^ _106147) ^ [] : [-(on_path(_121040, _120847))], (436 ^ _106147) ^ [] : [-(on_path(_121038, _120847))], (438 ^ _106147) ^ [] : [448 ^ _106147 : [(449 ^ _106147) ^ [] : [-(sequential(_121040, 447 ^ [_120843, _120845, _120847, _121038, _121040]))], (451 ^ _106147) ^ [] : [-(precedes(447 ^ [_120843, _120845, _120847, _121038, _121040], _121038, _120847))], (453 ^ _106147) ^ [] : [sequential(_121040, _121038)]], 439 ^ _106147 : [(440 ^ _106147) ^ [] : [-(sequential(_121040, _121038))], (442 ^ _106147) ^ [_121481] : [sequential(_121040, _121481), precedes(_121481, _121038, _120847)]]]]]]], (486 ^ _106147) ^ [_123184, _123186, _123188, _123190, _123192] : [shortest_path(_123192, _123190, _123184), precedes(_123188, _123186, _123184), 493 ^ _106147 : [(500 ^ _106147) ^ [] : [precedes(_123186, _123188, _123184)], (494 ^ _106147) ^ [_123477] : [tail_of(_123477) = tail_of(_123188), head_of(_123477) = head_of(_123186)]]], (455 ^ _106147) ^ [_122083, _122085, _122087] : [shortest_path(_122087, _122085, _122083), 458 ^ _106147 : [(459 ^ _106147) ^ [] : [-(path(_122087, _122085, _122083))], (461 ^ _106147) ^ [] : [_122087 = _122085], (463 ^ _106147) ^ [_122382] : [path(_122087, _122085, _122382), -(less_or_equal(length_of(_122083), length_of(_122382)))]]], (469 ^ _106147) ^ [_122581, _122583, _122585] : [-(shortest_path(_122585, _122583, _122581)), path(_122585, _122583, _122581), -(_122585 = _122583), 479 ^ _106147 : [(480 ^ _106147) ^ [] : [-(path(_122585, _122583, 478 ^ [_122581, _122583, _122585]))], (482 ^ _106147) ^ [] : [less_or_equal(length_of(_122581), length_of(478 ^ [_122581, _122583, _122585]))]]]], input).
% 137.68/132.89  ncf('1',plain,[triangle(598 ^ [], 599 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])],start(608 ^ 0,bind([[_127859], [587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]]))).
% 137.68/132.89  ncf('1.1',plain,[-(triangle(598 ^ [], 599 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])), edge(598 ^ []), edge(599 ^ []), edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), sequential(598 ^ [], 599 ^ []), sequential(599 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), sequential(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], 598 ^ [])],extension(518 ^ 1,bind([[_124409, _124411, _124413], [587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], 599 ^ [], 598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1',plain,[-(edge(598 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), on_path(598 ^ [], 600 ^ [])],extension(339 ^ 2,bind([[_117819, _117821, _117823, _117825], [598 ^ [], 600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 3,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 4,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 5,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), shortest_path(596 ^ [], 597 ^ [], 600 ^ [])],extension(455 ^ 6,bind([[_122083, _122085, _122087], [600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.1.1.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 7)).
% 137.68/132.89  ncf('1.1.1.1.1.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 6,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 6,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 6,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 5,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 5,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 5,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 4,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 4,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 4,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2',plain,[-(on_path(598 ^ [], 600 ^ [])), on_path(598 ^ [], 600 ^ []), 598 ^ [] = 598 ^ [], 600 ^ [] = 600 ^ []],extension(62 ^ 3,bind([[_108291, _108293, _108295, _108297], [600 ^ [], 600 ^ [], 598 ^ [], 598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.1',plain,[-(on_path(598 ^ [], 600 ^ [])), on_path(598 ^ [], 600 ^ []), 598 ^ [] = 598 ^ [], 600 ^ [] = 600 ^ []],extension(62 ^ 4,bind([[_108291, _108293, _108295, _108297], [600 ^ [], 600 ^ [], 598 ^ [], 598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.1.1',plain,[-(on_path(598 ^ [], 600 ^ [])), 430 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 430 : path(596 ^ [], 597 ^ [], 600 ^ [])],extension(426 ^ 5,bind([[_120843, _120845, _120847, _121038, _121040], [597 ^ [], 596 ^ [], 600 ^ [], 599 ^ [], 598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.1.1.1',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 8)).
% 137.68/132.89  ncf('1.1.1.2.1.1.2',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), shortest_path(596 ^ [], 597 ^ [], 600 ^ [])],extension(455 ^ 6,bind([[_122083, _122085, _122087], [600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.1.1.2.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 7)).
% 137.68/132.89  ncf('1.1.1.2.1.2',plain,[-(598 ^ [] = 598 ^ [])],extension(2 ^ 5,bind([[_106291], [598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.1.3',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 5,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.2',plain,[-(598 ^ [] = 598 ^ [])],extension(2 ^ 4,bind([[_106291], [598 ^ []]]))).
% 137.68/132.89  ncf('1.1.1.2.3',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 4,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.2',plain,[-(edge(599 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), on_path(599 ^ [], 600 ^ [])],extension(339 ^ 2,bind([[_117819, _117821, _117823, _117825], [599 ^ [], 600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 3,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 4,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 5,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), shortest_path(596 ^ [], 597 ^ [], 600 ^ [])],extension(455 ^ 6,bind([[_122083, _122085, _122087], [600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.1.1.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 7)).
% 137.68/132.89  ncf('1.1.2.1.1.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 6,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 6,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 6,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 5,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 5,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 5,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 4,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 4,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 4,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2',plain,[-(on_path(599 ^ [], 600 ^ [])), 430 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 430 : path(596 ^ [], 597 ^ [], 600 ^ [])],extension(426 ^ 3,bind([[_120843, _120845, _120847, _121038, _121040], [597 ^ [], 596 ^ [], 600 ^ [], 599 ^ [], 598 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.1',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 6)).
% 137.68/132.89  ncf('1.1.2.2.2',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 4,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), path(596 ^ [], 597 ^ [], 600 ^ []), 596 ^ [] = 596 ^ [], 597 ^ [] = 597 ^ [], 600 ^ [] = 600 ^ []],extension(44 ^ 5,bind([[_107710, _107712, _107714, _107716, _107718, _107720], [600 ^ [], 600 ^ [], 597 ^ [], 597 ^ [], 596 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.1.1',plain,[-(path(596 ^ [], 597 ^ [], 600 ^ [])), shortest_path(596 ^ [], 597 ^ [], 600 ^ [])],extension(455 ^ 6,bind([[_122083, _122085, _122087], [600 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.1.1.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 7)).
% 137.68/132.89  ncf('1.1.2.2.2.1.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 6,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.1.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 6,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.1.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 6,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.2',plain,[-(596 ^ [] = 596 ^ [])],extension(2 ^ 5,bind([[_106291], [596 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.3',plain,[-(597 ^ [] = 597 ^ [])],extension(2 ^ 5,bind([[_106291], [597 ^ []]]))).
% 137.68/132.89  ncf('1.1.2.2.2.4',plain,[-(600 ^ [] = 600 ^ [])],extension(2 ^ 5,bind([[_106291], [600 ^ []]]))).
% 137.68/132.89  ncf('1.1.3',plain,[-(edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])), 580 : shortest_path(596 ^ [], 597 ^ [], 600 ^ []), 580 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 580 : complete],extension(576 ^ 2,bind([[_126597, _126599, _126601, _126603, _126605], [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.3.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 5)).
% 137.68/132.89  ncf('1.1.3.2',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 5)).
% 137.68/132.89  ncf('1.1.3.3',plain,[-(complete)],extension(595 ^ 3)).
% 137.68/132.89  ncf('1.1.4',plain,[-(sequential(598 ^ [], 599 ^ []))],extension(606 ^ 2)).
% 137.68/132.89  ncf('1.1.5',plain,[-(sequential(599 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])), edge(599 ^ []), edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), -(599 ^ [] = 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), head_of(599 ^ []) = tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])],extension(384 ^ 2,bind([[_119441, _119443], [587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], 599 ^ []]]))).
% 137.68/132.89  ncf('1.1.5.1',plain,[-(edge(599 ^ []))],lemmata('[1].x')).
% 137.68/132.89  ncf('1.1.5.2',plain,[-(edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],lemmata('[1].x')).
% 137.68/132.89  ncf('1.1.5.3',plain,[599 ^ [] = 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], -(head_of(599 ^ []) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],extension(204 ^ 3,bind([[_113016, _113018], [587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], 599 ^ []]]))).
% 137.68/132.89  ncf('1.1.5.3.1',plain,[head_of(599 ^ []) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), -(tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])), tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(599 ^ [])],extension(10 ^ 4,bind([[_106602, _106604, _106606], [head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), head_of(599 ^ []), tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])]]))).
% 137.68/132.89  ncf('1.1.5.3.1.1',plain,[tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), -(head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],extension(4 ^ 5,bind([[_106398, _106400], [head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])]]))).
% 137.68/132.89  ncf('1.1.5.3.1.1.1',plain,[head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])],extension(216 ^ 6,bind([[_113460], [587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]]))).
% 137.68/132.89  ncf('1.1.5.3.1.1.1.1',plain,[-(edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],lemmata('[1, 1].x')).
% 137.68/132.89  ncf('1.1.5.3.1.2',plain,[-(tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(599 ^ [])), 580 : shortest_path(596 ^ [], 597 ^ [], 600 ^ []), 580 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 580 : complete],extension(576 ^ 5,bind([[_126597, _126599, _126601, _126603, _126605], [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.5.3.1.2.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 8)).
% 137.68/132.89  ncf('1.1.5.3.1.2.2',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 8)).
% 137.68/132.89  ncf('1.1.5.3.1.2.3',plain,[-(complete)],extension(595 ^ 6)).
% 137.68/132.89  ncf('1.1.5.4',plain,[-(head_of(599 ^ []) = tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])), tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(599 ^ [])],extension(4 ^ 3,bind([[_106398, _106400], [head_of(599 ^ []), tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])]]))).
% 137.68/132.89  ncf('1.1.5.4.1',plain,[-(tail_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(599 ^ [])), 580 : shortest_path(596 ^ [], 597 ^ [], 600 ^ []), 580 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 580 : complete],extension(576 ^ 4,bind([[_126597, _126599, _126601, _126603, _126605], [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.5.4.1.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 7)).
% 137.68/132.89  ncf('1.1.5.4.1.2',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 7)).
% 137.68/132.89  ncf('1.1.5.4.1.3',plain,[-(complete)],extension(595 ^ 5)).
% 137.68/132.89  ncf('1.1.6',plain,[-(sequential(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []], 598 ^ [])), edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), edge(598 ^ []), -(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []] = 598 ^ []), head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(598 ^ [])],extension(384 ^ 2,bind([[_119441, _119443], [598 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]]))).
% 137.68/132.89  ncf('1.1.6.1',plain,[-(edge(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],lemmata('[1].x')).
% 137.68/132.89  ncf('1.1.6.2',plain,[-(edge(598 ^ []))],lemmata('[1].x')).
% 137.68/132.89  ncf('1.1.6.3',plain,[587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []] = 598 ^ [], -(head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(598 ^ []))],extension(204 ^ 3,bind([[_113016, _113018], [598 ^ [], 587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]]))).
% 137.68/132.89  ncf('1.1.6.3.1',plain,[head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = head_of(598 ^ []), -(head_of(598 ^ []) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]))],extension(4 ^ 4,bind([[_106398, _106400], [head_of(598 ^ []), head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []])]]))).
% 137.68/132.89  ncf('1.1.6.3.1.1',plain,[head_of(598 ^ []) = head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), -(head_of(598 ^ []) = tail_of(598 ^ [])), head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(598 ^ [])],extension(10 ^ 5,bind([[_106602, _106604, _106606], [tail_of(598 ^ []), head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]), head_of(598 ^ [])]]))).
% 137.68/132.89  ncf('1.1.6.3.1.1.1',plain,[head_of(598 ^ []) = tail_of(598 ^ []), edge(598 ^ [])],extension(216 ^ 6,bind([[_113460], [598 ^ []]]))).
% 137.68/132.89  ncf('1.1.6.3.1.1.1.1',plain,[-(edge(598 ^ []))],lemmata('[1, 1].x')).
% 137.68/132.89  ncf('1.1.6.3.1.1.2',plain,[-(head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(598 ^ [])), 580 : shortest_path(596 ^ [], 597 ^ [], 600 ^ []), 580 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 580 : complete],extension(576 ^ 6,bind([[_126597, _126599, _126601, _126603, _126605], [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.6.3.1.1.2.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 9)).
% 137.68/132.89  ncf('1.1.6.3.1.1.2.2',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 9)).
% 137.68/132.89  ncf('1.1.6.3.1.1.2.3',plain,[-(complete)],extension(595 ^ 7)).
% 137.68/132.89  ncf('1.1.6.4',plain,[-(head_of(587 ^ [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]) = tail_of(598 ^ [])), 580 : shortest_path(596 ^ [], 597 ^ [], 600 ^ []), 580 : precedes(598 ^ [], 599 ^ [], 600 ^ []), 580 : complete],extension(576 ^ 3,bind([[_126597, _126599, _126601, _126603, _126605], [600 ^ [], 599 ^ [], 598 ^ [], 597 ^ [], 596 ^ []]]))).
% 137.68/132.89  ncf('1.1.6.4.1',plain,[-(shortest_path(596 ^ [], 597 ^ [], 600 ^ []))],extension(602 ^ 6)).
% 137.68/132.89  ncf('1.1.6.4.2',plain,[-(precedes(598 ^ [], 599 ^ [], 600 ^ []))],extension(604 ^ 6)).
% 137.68/132.89  ncf('1.1.6.4.3',plain,[-(complete)],extension(595 ^ 4)).
% 137.68/132.89  %-----------------------------------------------------
% 137.68/132.89  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------