%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 12:02:49 EDT 2023

% Result   : Theorem 46.45s 45.84s
% Output   : Proof 46.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 12:29:47 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 46.45/45.84  
% 46.45/45.84  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 46.45/45.84  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.45/45.84  %-----------------------------------------------------
% 46.45/45.84  ncf(matrix, plain, [(671 ^ _127718) ^ [] : [681 ^ _127718 : [(686 ^ _127718) ^ [] : [-(being_limit_ordinal(667 ^ []))], (684 ^ _127718) ^ [] : [-(667 ^ [] = succ(680 ^ []))], (682 ^ _127718) ^ [] : [-(ordinal(680 ^ []))]], 672 ^ _127718 : [(675 ^ _127718) ^ [_127912] : [ordinal(_127912), 667 ^ [] = succ(_127912)], (673 ^ _127718) ^ [] : [being_limit_ordinal(667 ^ [])]]], (669 ^ _127718) ^ [] : [-(ordinal(667 ^ []))], !, (344 ^ _106877) ^ [] : [true___, -(true___)], (531 ^ _106877) ^ [_123083] : [-(in(_123083, succ(_123083)))], (429 ^ _106877) ^ [] : [-(epsilon_connected(425 ^ []))], (457 ^ _106877) ^ [] : [-(epsilon_transitive(447 ^ []))], (170 ^ _106877) ^ [_112185, _112187] : [-(being_limit_ordinal(_112185)), _112187 = _112185, being_limit_ordinal(_112187)], (314 ^ _106877) ^ [] : [true___, -(true___)], (379 ^ _106877) ^ [_118402, _118404] : [-(relation(set_union2(_118404, _118402))), relation(_118404), relation(_118402)], (488 ^ _106877) ^ [] : [-(relation(486 ^ []))], (646 ^ _106877) ^ [_126722] : [empty(_126722), -(_126722 = empty_set)], (240 ^ _106877) ^ [_114588] : [251 ^ _106877 : [(256 ^ _106877) ^ [] : [-(one_to_one(_114588))], (254 ^ _106877) ^ [] : [-(function(_114588))], (252 ^ _106877) ^ [] : [-(relation(_114588))]], relation(_114588), empty(_114588), function(_114588)], (389 ^ _106877) ^ [_118701, _118703] : [-(empty(_118703)), empty(set_union2(_118703, _118701))], (4 ^ _106877) ^ [_107108, _107110] : [_107110 = _107108, -(_107108 = _107110)], (424 ^ _106877) ^ [] : [-(function(420 ^ []))], (304 ^ _106877) ^ [_116530, _116532] : [-(proper_subset(_116532, _116530)), subset(_116532, _116530), -(_116532 = _116530)], (439 ^ _106877) ^ [] : [-(empty(437 ^ []))], (495 ^ _106877) ^ [] : [-(relation_empty_yielding(491 ^ []))], (186 ^ _106877) ^ [_112758, _112760, _112762, _112764] : [-(set_union2(_112764, _112760) = set_union2(_112762, _112758)), _112764 = _112762, _112760 = _112758], (353 ^ _106877) ^ [] : [-(empty(empty_set))], (268 ^ _106877) ^ [_115350] : [empty(_115350), 271 ^ _106877 : [(276 ^ _106877) ^ [] : [-(ordinal(_115350))], (274 ^ _106877) ^ [] : [-(epsilon_connected(_115350))], (272 ^ _106877) ^ [] : [-(epsilon_transitive(_115350))]]], (10 ^ _106877) ^ [_107312, _107314, _107316] : [-(_107316 = _107312), _107316 = _107314, _107314 = _107312], (658 ^ _106877) ^ [_127111, _127113] : [empty(_127113), -(_127113 = _127111), empty(_127111)], (474 ^ _106877) ^ [] : [-(function(470 ^ []))], (94 ^ _106877) ^ [_109867, _109869, _109871, _109873] : [-(ordinal_subset(_109871, _109867)), ordinal_subset(_109873, _109869), _109873 = _109871, _109869 = _109867], (431 ^ _106877) ^ [] : [-(ordinal(425 ^ []))], (407 ^ _106877) ^ [_119331, _119333] : [-(empty(_119333)), empty(set_union2(_119331, _119333))], (535 ^ _106877) ^ [_123273, _123275] : [in(_123275, _123273), -(element(_123275, _123273))], (214 ^ _106877) ^ [_113762, _113764] : [proper_subset(_113764, _113762), proper_subset(_113762, _113764)], (417 ^ _106877) ^ [_119640, _119642] : [-(set_union2(_119642, _119642) = _119642)], (466 ^ _106877) ^ [] : [-(relation(462 ^ []))], (415 ^ _106877) ^ [] : [-(relation(empty_set))], (585 ^ _106877) ^ [_124831, _124833] : [element(_124833, powerset(_124831)), -(subset(_124833, _124831))], (434 ^ _106877) ^ [] : [-(empty(432 ^ []))], (451 ^ _106877) ^ [] : [-(function(447 ^ []))], (371 ^ _106877) ^ [] : [-(empty(empty_set))], (444 ^ _106877) ^ [] : [-(empty(440 ^ []))], (160 ^ _106877) ^ [_111910, _111912] : [-(ordinal(_111910)), _111912 = _111910, ordinal(_111912)], (555 ^ _106877) ^ [_123909, _123911] : [element(_123911, _123909), -(empty(_123909)), -(in(_123911, _123909))], (363 ^ _106877) ^ [] : [-(relation(empty_set))], (367 ^ _106877) ^ [] : [-(function(empty_set))], (180 ^ _106877) ^ [_112512, _112514] : [_112514 = _112512, -(singleton(_112514) = singleton(_112512))], (591 ^ _106877) ^ [_124997, _124999] : [subset(_124999, _124997), -(element(_124999, powerset(_124997)))], (626 ^ _106877) ^ [_126099, _126101, _126103] : [-(element(_126103, _126099)), in(_126103, _126101), element(_126101, powerset(_126099))], (499 ^ _106877) ^ [_122176, _122178] : [ordinal(_122178), ordinal(_122176), 506 ^ _106877 : [(513 ^ _106877) ^ [] : [subset(_122178, _122176), -(ordinal_subset(_122178, _122176))], (507 ^ _106877) ^ [] : [ordinal_subset(_122178, _122176), -(subset(_122178, _122176))]]], (332 ^ _106877) ^ [] : [true___, -(true___)], (597 ^ _106877) ^ [_125199] : [ordinal(_125199), 600 ^ _106877 : [(601 ^ _106877) ^ [] : [being_limit_ordinal(_125199), 604 ^ _106877 : [(605 ^ _106877) ^ [_125445] : [ordinal(_125445), in(_125445, _125199), -(in(succ(_125445), _125199))]]], (615 ^ _106877) ^ [] : [617 ^ _106877 : [(622 ^ _106877) ^ [] : [in(succ(616 ^ [_125199]), _125199)], (620 ^ _106877) ^ [] : [-(in(616 ^ [_125199], _125199))], (618 ^ _106877) ^ [] : [-(ordinal(616 ^ [_125199]))]], -(being_limit_ordinal(_125199))]]], (359 ^ _106877) ^ [_117803] : [empty(succ(_117803))], (479 ^ _106877) ^ [] : [empty(477 ^ [])], (338 ^ _106877) ^ [] : [true___, -(true___)], (361 ^ _106877) ^ [] : [-(empty(empty_set))], (636 ^ _106877) ^ [_126426, _126428, _126430] : [in(_126430, _126428), element(_126428, powerset(_126426)), empty(_126426)], (294 ^ _106877) ^ [_116149] : [-(succ(_116149) = set_union2(_116149, singleton(_116149)))], (136 ^ _106877) ^ [_111199, _111201, _111203, _111205] : [-(in(_111203, _111199)), in(_111205, _111201), _111205 = _111203, _111201 = _111199], (422 ^ _106877) ^ [] : [-(relation(420 ^ []))], (419 ^ _106877) ^ [_119736, _119738] : [proper_subset(_119738, _119738)], (476 ^ _106877) ^ [] : [-(one_to_one(470 ^ []))], (446 ^ _106877) ^ [] : [-(function(440 ^ []))], (493 ^ _106877) ^ [] : [-(relation(491 ^ []))], (369 ^ _106877) ^ [] : [-(one_to_one(empty_set))], (436 ^ _106877) ^ [] : [-(relation(432 ^ []))], (234 ^ _106877) ^ [_114402] : [empty(_114402), -(relation(_114402))], (30 ^ _106877) ^ [_107920, _107922] : [-(epsilon_connected(_107920)), _107922 = _107920, epsilon_connected(_107922)], (80 ^ _106877) ^ [_109423, _109425, _109427, _109429] : [-(proper_subset(_109427, _109423)), proper_subset(_109429, _109425), _109429 = _109427, _109425 = _109423], (355 ^ _106877) ^ [] : [-(relation(empty_set))], (464 ^ _106877) ^ [] : [empty(462 ^ [])], (50 ^ _106877) ^ [_108510, _108512] : [-(relation_empty_yielding(_108510)), _108512 = _108510, relation_empty_yielding(_108512)], (485 ^ _106877) ^ [] : [-(ordinal(477 ^ []))], (280 ^ _106877) ^ [_115791, _115793] : [ordinal(_115793), ordinal(_115791), -(ordinal_subset(_115793, _115791)), -(ordinal_subset(_115791, _115793))], (497 ^ _106877) ^ [] : [-(function(491 ^ []))], (375 ^ _106877) ^ [] : [-(epsilon_connected(empty_set))], (220 ^ _106877) ^ [_113959] : [empty(_113959), -(function(_113959))], (296 ^ _106877) ^ [_116292, _116294] : [proper_subset(_116294, _116292), 299 ^ _106877 : [(302 ^ _106877) ^ [] : [_116294 = _116292], (300 ^ _106877) ^ [] : [-(subset(_116294, _116292))]]], (40 ^ _106877) ^ [_108215, _108217] : [-(relation(_108215)), _108217 = _108215, relation(_108217)], (395 ^ _106877) ^ [_118903] : [ordinal(_118903), 398 ^ _106877 : [(401 ^ _106877) ^ [] : [-(epsilon_transitive(succ(_118903)))], (403 ^ _106877) ^ [] : [-(epsilon_connected(succ(_118903)))], (405 ^ _106877) ^ [] : [-(ordinal(succ(_118903)))], (399 ^ _106877) ^ [] : [empty(succ(_118903))]]], (60 ^ _106877) ^ [_108805, _108807] : [-(function(_108805)), _108807 = _108805, function(_108807)], (413 ^ _106877) ^ [] : [-(empty(empty_set))], (351 ^ _106877) ^ [_117558] : [-(element(349 ^ [_117558], _117558))], (427 ^ _106877) ^ [] : [-(epsilon_transitive(425 ^ []))], (278 ^ _106877) ^ [_115676, _115678] : [-(set_union2(_115678, _115676) = set_union2(_115676, _115678))], (490 ^ _106877) ^ [] : [-(relation_empty_yielding(486 ^ []))], (453 ^ _106877) ^ [] : [-(one_to_one(447 ^ []))], (519 ^ _106877) ^ [_122723, _122725] : [-(ordinal_subset(_122725, _122725)), ordinal(_122725), ordinal(_122723)], (442 ^ _106877) ^ [] : [-(relation(440 ^ []))], (196 ^ _106877) ^ [_113089, _113091] : [_113091 = _113089, -(powerset(_113091) = powerset(_113089))], (202 ^ _106877) ^ [_113287, _113289] : [_113289 = _113287, -(succ(_113289) = succ(_113287))], (373 ^ _106877) ^ [] : [-(epsilon_transitive(empty_set))], (455 ^ _106877) ^ [] : [-(empty(447 ^ []))], (320 ^ _106877) ^ [] : [true___, -(true___)], (469 ^ _106877) ^ [] : [empty(467 ^ [])], (449 ^ _106877) ^ [] : [-(relation(447 ^ []))], (150 ^ _106877) ^ [_111615, _111617] : [-(empty(_111615)), _111617 = _111615, empty(_111617)], (483 ^ _106877) ^ [] : [-(epsilon_connected(477 ^ []))], (208 ^ _106877) ^ [_113551, _113553] : [in(_113553, _113551), in(_113551, _113553)], (357 ^ _106877) ^ [] : [-(relation_empty_yielding(empty_set))], (481 ^ _106877) ^ [] : [-(epsilon_transitive(477 ^ []))], (529 ^ _106877) ^ [_123003, _123005] : [-(subset(_123005, _123005))], (652 ^ _106877) ^ [_126924, _126926] : [in(_126926, _126924), empty(_126924)], (365 ^ _106877) ^ [] : [-(relation_empty_yielding(empty_set))], (565 ^ _106877) ^ [_124193] : [ordinal(_124193), 568 ^ _106877 : [(569 ^ _106877) ^ [_124331] : [ordinal(_124331), 572 ^ _106877 : [(579 ^ _106877) ^ [] : [ordinal_subset(succ(_124193), _124331), -(in(_124193, _124331))], (573 ^ _106877) ^ [] : [in(_124193, _124331), -(ordinal_subset(succ(_124193), _124331))]]]]], (258 ^ _106877) ^ [_115081] : [-(ordinal(_115081)), epsilon_transitive(_115081), epsilon_connected(_115081)], (122 ^ _106877) ^ [_110755, _110757, _110759, _110761] : [-(element(_110759, _110755)), element(_110761, _110757), _110761 = _110759, _110757 = _110755], (20 ^ _106877) ^ [_107625, _107627] : [-(one_to_one(_107625)), _107627 = _107625, one_to_one(_107627)], (541 ^ _106877) ^ [_123469] : [epsilon_transitive(_123469), 544 ^ _106877 : [(545 ^ _106877) ^ [_123605] : [ordinal(_123605), proper_subset(_123469, _123605), -(in(_123469, _123605))]]], (377 ^ _106877) ^ [] : [-(ordinal(empty_set))], (533 ^ _106877) ^ [_123163] : [-(set_union2(_123163, empty_set) = _123163)], (2 ^ _106877) ^ [_107001] : [-(_107001 = _107001)], (459 ^ _106877) ^ [] : [-(epsilon_connected(447 ^ []))], (472 ^ _106877) ^ [] : [-(relation(470 ^ []))], (226 ^ _106877) ^ [_114145] : [ordinal(_114145), 229 ^ _106877 : [(232 ^ _106877) ^ [] : [-(epsilon_connected(_114145))], (230 ^ _106877) ^ [] : [-(epsilon_transitive(_114145))]]], (326 ^ _106877) ^ [] : [true___, -(true___)], (70 ^ _106877) ^ [_109100, _109102] : [-(epsilon_transitive(_109100)), _109102 = _109100, epsilon_transitive(_109102)], (461 ^ _106877) ^ [] : [-(ordinal(447 ^ []))], (108 ^ _106877) ^ [_110311, _110313, _110315, _110317] : [-(subset(_110315, _110311)), subset(_110317, _110313), _110317 = _110315, _110313 = _110311]], input).
% 46.45/45.84  ncf('1',plain,[686 : -(being_limit_ordinal(667 ^ [])), 673 : being_limit_ordinal(667 ^ [])],start(671 ^ 0)).
% 46.45/45.84  ncf('1.1',plain,[being_limit_ordinal(667 ^ []), -(being_limit_ordinal(667 ^ [])), 667 ^ [] = 667 ^ []],extension(170 ^ 3,bind([[_112185, _112187], [667 ^ [], 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.1',plain,[being_limit_ordinal(667 ^ []), -(being_limit_ordinal(succ(680 ^ []))), 667 ^ [] = succ(680 ^ [])],extension(170 ^ 4,bind([[_112185, _112187], [succ(680 ^ []), 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1',plain,[being_limit_ordinal(succ(680 ^ [])), -(being_limit_ordinal(667 ^ [])), succ(680 ^ []) = 667 ^ []],extension(170 ^ 5,bind([[_112185, _112187], [667 ^ [], succ(680 ^ [])]]))).
% 46.45/45.84  ncf('1.1.1.1.1',plain,[being_limit_ordinal(667 ^ []), -(being_limit_ordinal(succ(680 ^ []))), 667 ^ [] = succ(680 ^ [])],extension(170 ^ 6,bind([[_112185, _112187], [succ(680 ^ []), 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1.1.1',plain,[being_limit_ordinal(succ(680 ^ [])), 605 : ordinal(680 ^ []), 605 : in(680 ^ [], succ(680 ^ [])), 605 : -(in(succ(680 ^ []), succ(680 ^ []))), 601 : ordinal(succ(680 ^ []))],extension(597 ^ 7,bind([[_125199, _125445], [succ(680 ^ []), 680 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1.1.1.1',plain,[-(ordinal(680 ^ []))],extension(682 ^ 12)).
% 46.45/45.84  ncf('1.1.1.1.1.1.2',plain,[-(in(680 ^ [], succ(680 ^ [])))],extension(531 ^ 12,bind([[_123083], [680 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1.1.1.3',plain,[in(succ(680 ^ []), succ(680 ^ [])), in(succ(680 ^ []), succ(680 ^ []))],extension(208 ^ 12,bind([[_113551, _113553], [succ(680 ^ []), succ(680 ^ [])]]))).
% 46.45/45.84  ncf('1.1.1.1.1.1.3.1',plain,[-(in(succ(680 ^ []), succ(680 ^ [])))],reduction('1.1.1.1.1.1')).
% 46.45/45.84  ncf('1.1.1.1.1.1.4',plain,[-(ordinal(succ(680 ^ []))), 667 ^ [] = succ(680 ^ []), ordinal(667 ^ [])],extension(160 ^ 8,bind([[_111910, _111912], [succ(680 ^ []), 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1.1.1.4.1',plain,[-(667 ^ [] = succ(680 ^ []))],extension(684 ^ 9)).
% 46.45/45.84  ncf('1.1.1.1.1.1.4.2',plain,[-(ordinal(667 ^ []))],extension(669 ^ 9)).
% 46.45/45.84  ncf('1.1.1.1.1.2',plain,[-(667 ^ [] = succ(680 ^ []))],extension(684 ^ 7)).
% 46.45/45.84  ncf('1.1.1.1.2',plain,[-(succ(680 ^ []) = 667 ^ []), 667 ^ [] = succ(680 ^ [])],extension(4 ^ 6,bind([[_107108, _107110], [succ(680 ^ []), 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.1.1.2.1',plain,[-(667 ^ [] = succ(680 ^ []))],extension(684 ^ 7)).
% 46.45/45.84  ncf('1.1.1.2',plain,[-(667 ^ [] = succ(680 ^ []))],extension(684 ^ 5)).
% 46.45/45.84  ncf('1.1.2',plain,[-(667 ^ [] = 667 ^ []), -(proper_subset(667 ^ [], 667 ^ [])), subset(667 ^ [], 667 ^ [])],extension(304 ^ 4,bind([[_116530, _116532], [667 ^ [], 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.2.1',plain,[proper_subset(667 ^ [], 667 ^ []), proper_subset(667 ^ [], 667 ^ [])],extension(214 ^ 5,bind([[_113762, _113764], [667 ^ [], 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.2.1.1',plain,[-(proper_subset(667 ^ [], 667 ^ []))],reduction('1.1.2')).
% 46.45/45.84  ncf('1.1.2.2',plain,[-(subset(667 ^ [], 667 ^ [])), 507 : ordinal_subset(667 ^ [], 667 ^ []), 507 : ordinal(667 ^ []), 507 : ordinal(667 ^ [])],extension(499 ^ 5,bind([[_122176, _122178], [667 ^ [], 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.2.2.1',plain,[-(ordinal_subset(667 ^ [], 667 ^ [])), ordinal(667 ^ []), ordinal(667 ^ []), -(ordinal_subset(667 ^ [], 667 ^ []))],extension(280 ^ 8,bind([[_115791, _115793], [667 ^ [], 667 ^ []]]))).
% 46.45/45.84  ncf('1.1.2.2.1.1',plain,[-(ordinal(667 ^ []))],extension(669 ^ 9)).
% 46.45/45.84  ncf('1.1.2.2.1.2',plain,[-(ordinal(667 ^ []))],lemmata('[2, 2, 1, 1].x')).
% 46.45/45.84  ncf('1.1.2.2.1.3',plain,[ordinal_subset(667 ^ [], 667 ^ [])],reduction('1.1.2.2')).
% 46.45/45.84  ncf('1.1.2.2.2',plain,[-(ordinal(667 ^ []))],extension(669 ^ 6)).
% 46.45/45.84  ncf('1.1.2.2.3',plain,[-(ordinal(667 ^ []))],lemmata('[2, 1, 1].x')).
% 46.45/45.84  ncf('1.2',plain,[-(being_limit_ordinal(667 ^ [])), 622 : in(succ(616 ^ [667 ^ []]), 667 ^ []), 615 : ordinal(667 ^ [])],extension(597 ^ 3,bind([[_125199], [667 ^ []]]))).
% 46.45/45.84  ncf('1.2.1',plain,[-(in(succ(616 ^ [667 ^ []]), 667 ^ [])), 545 : ordinal(667 ^ []), 545 : proper_subset(succ(616 ^ [667 ^ []]), 667 ^ []), 545 : epsilon_transitive(succ(616 ^ [667 ^ []]))],extension(541 ^ 8,bind([[_123469, _123605], [succ(616 ^ [667 ^ []]), 667 ^ []]]))).
% 46.45/45.84  ncf('1.2.1.1',plain,[-(ordinal(667 ^ []))],extension(669 ^ 11)).
% 46.45/45.84  ncf('1.2.1.2',plain,[-(proper_subset(succ(616 ^ [667 ^ []]), 667 ^ [])), subset(succ(616 ^ [667 ^ []]), 667 ^ []), -(succ(616 ^ [667 ^ []]) = 667 ^ [])],extension(304 ^ 11,bind([[_116530, _116532], [667 ^ [], succ(616 ^ [667 ^ []])]]))).
% 46.45/45.84  ncf('1.2.1.2.1',plain,[-(subset(succ(616 ^ [667 ^ []]), 667 ^ [])), 507 : ordinal_subset(succ(616 ^ [667 ^ []]), 667 ^ []), 507 : ordinal(succ(616 ^ [667 ^ []])), 507 : ordinal(667 ^ [])],extension(499 ^ 12,bind([[_122176, _122178], [667 ^ [], succ(616 ^ [667 ^ []])]]))).
% 46.45/45.84  ncf('1.2.1.2.1.1',plain,[-(ordinal_subset(succ(616 ^ [667 ^ []]), 667 ^ [])), 573 : in(616 ^ [667 ^ []], 667 ^ []), 573 : ordinal(667 ^ []), 569 : ordinal(616 ^ [667 ^ []])],extension(565 ^ 15,bind([[_124193, _124331], [616 ^ [667 ^ []], 667 ^ []]]))).
% 46.45/45.84  ncf('1.2.1.2.1.1.1',plain,[-(in(616 ^ [667 ^ []], 667 ^ []))],extension(620 ^ 20)).
% 46.45/45.84  ncf('1.2.1.2.1.1.2',plain,[-(ordinal(667 ^ []))],lemmata('[2, 1].x')).
% 46.45/45.84  ncf('1.2.1.2.1.1.3',plain,[-(ordinal(616 ^ [667 ^ []]))],extension(618 ^ 16)).
% 46.45/45.84  ncf('1.2.1.2.1.2',plain,[-(ordinal(succ(616 ^ [667 ^ []]))), ordinal(616 ^ [667 ^ []])],extension(395 ^ 13,bind([[_118903], [616 ^ [667 ^ []]]]))).
% 46.45/45.84  ncf('1.2.1.2.1.2.1',plain,[-(ordinal(616 ^ [667 ^ []]))],extension(618 ^ 14)).
% 46.45/45.84  ncf('1.2.1.2.1.3',plain,[-(ordinal(667 ^ []))],lemmata('[2, 1].x')).
% 46.45/45.84  ncf('1.2.1.2.2',plain,[succ(616 ^ [667 ^ []]) = 667 ^ [], -(667 ^ [] = succ(616 ^ [667 ^ []]))],extension(4 ^ 12,bind([[_107108, _107110], [667 ^ [], succ(616 ^ [667 ^ []])]]))).
% 46.45/45.84  ncf('1.2.1.2.2.1',plain,[667 ^ [] = succ(616 ^ [667 ^ []]), ordinal(616 ^ [667 ^ []])],extension(675 ^ 13,bind([[_127912], [616 ^ [667 ^ []]]]))).
% 46.45/45.84  ncf('1.2.1.2.2.1.1',plain,[-(ordinal(616 ^ [667 ^ []]))],extension(618 ^ 14)).
% 46.45/45.84  ncf('1.2.1.3',plain,[-(epsilon_transitive(succ(616 ^ [667 ^ []]))), ordinal(616 ^ [667 ^ []])],extension(395 ^ 9,bind([[_118903], [616 ^ [667 ^ []]]]))).
% 46.45/45.84  ncf('1.2.1.3.1',plain,[-(ordinal(616 ^ [667 ^ []]))],extension(618 ^ 10)).
% 46.45/45.84  ncf('1.2.2',plain,[-(ordinal(667 ^ []))],extension(669 ^ 4)).
% 46.45/45.84  %-----------------------------------------------------
% 46.45/45.84  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------