%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 11:44:32 EDT 2023

% Result   : Theorem 198.90s 192.56s
% Output   : Proof 198.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 17:23:59 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 198.90/192.56  
% 198.90/192.56  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 198.90/192.56  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 198.90/192.56  %-----------------------------------------------------
% 198.90/192.56  ncf(matrix, plain, [(539 ^ _108388) ^ [_108607] : [ordinal(_108607), -(in(_108607, 531 ^ []))], (533 ^ _108388) ^ [_108453] : [in(_108453, 531 ^ []), -(ordinal(_108453))], !, (400 ^ _91455) ^ [] : [-(function(396 ^ []))], (164 ^ _91455) ^ [_96595] : [empty(_96595), -(function(_96595))], (10 ^ _91455) ^ [_91890, _91892, _91894] : [-(_91894 = _91890), _91894 = _91892, _91892 = _91890], (365 ^ _91455) ^ [] : [-(empty(363 ^ []))], (409 ^ _91455) ^ [] : [-(epsilon_connected(403 ^ []))], (331 ^ _91455) ^ [] : [-(function(empty_set))], (345 ^ _91455) ^ [] : [-(relation(empty_set))], (353 ^ _91455) ^ [] : [-(epsilon_transitive(351 ^ []))], (426 ^ _91455) ^ [] : [-(relation(424 ^ []))], (337 ^ _91455) ^ [] : [-(epsilon_transitive(empty_set))], (321 ^ _91455) ^ [] : [-(relation(empty_set))], (184 ^ _91455) ^ [_97224] : [195 ^ _91455 : [(200 ^ _91455) ^ [] : [-(one_to_one(_97224))], (198 ^ _91455) ^ [] : [-(function(_97224))], (196 ^ _91455) ^ [] : [-(relation(_97224))]], relation(_97224), empty(_97224), function(_97224)], (152 ^ _91455) ^ [_96178, _96180] : [_96180 = _96178, -(powerset(_96180) = powerset(_96178))], (368 ^ _91455) ^ [] : [-(relation(366 ^ []))], (60 ^ _91455) ^ [_93383, _93385] : [-(relation(_93383)), _93385 = _93383, relation(_93385)], (355 ^ _91455) ^ [] : [-(epsilon_connected(351 ^ []))], (335 ^ _91455) ^ [] : [-(empty(empty_set))], (411 ^ _91455) ^ [] : [-(ordinal(403 ^ []))], (232 ^ _91455) ^ [_98642] : [234 ^ _91455 : [(237 ^ _91455) ^ [] : [subset(233 ^ [_98642], _98642)], (235 ^ _91455) ^ [] : [-(in(233 ^ [_98642], _98642))]], -(epsilon_transitive(_98642))], (4 ^ _91455) ^ [_91686, _91688] : [_91688 = _91686, -(_91686 = _91688)], (50 ^ _91455) ^ [_93088, _93090] : [-(relation_empty_yielding(_93088)), _93090 = _93088, relation_empty_yielding(_93090)], (298 ^ _91455) ^ [_101069] : [ordinal(_101069), 301 ^ _91455 : [(304 ^ _91455) ^ [] : [-(epsilon_connected(_101069))], (302 ^ _91455) ^ [] : [-(epsilon_transitive(_101069))]]], (343 ^ _91455) ^ [] : [-(empty(empty_set))], (357 ^ _91455) ^ [] : [-(ordinal(351 ^ []))], (370 ^ _91455) ^ [] : [-(empty(366 ^ []))], (170 ^ _91455) ^ [_96781] : [ordinal(_96781), 173 ^ _91455 : [(176 ^ _91455) ^ [] : [-(epsilon_connected(_96781))], (174 ^ _91455) ^ [] : [-(epsilon_transitive(_96781))]]], (90 ^ _91455) ^ [_94296, _94298, _94300, _94302] : [-(subset(_94300, _94296)), subset(_94302, _94298), _94302 = _94300, _94298 = _94296], (434 ^ _91455) ^ [_105095, _105097] : [in(_105097, _105095), -(element(_105097, _105095))], (279 ^ _91455) ^ [_100383, _100385] : [subset(_100385, _100383), 282 ^ _91455 : [(283 ^ _91455) ^ [_100520] : [in(_100520, _100385), -(in(_100520, _100383))]]], (516 ^ _91455) ^ [_107687, _107689] : [in(_107689, _107687), empty(_107687)], (289 ^ _91455) ^ [_100697, _100699] : [291 ^ _91455 : [(294 ^ _91455) ^ [] : [in(290 ^ [_100697, _100699], _100697)], (292 ^ _91455) ^ [] : [-(in(290 ^ [_100697, _100699], _100699))]], -(subset(_100699, _100697))], (395 ^ _91455) ^ [] : [empty(393 ^ [])], (325 ^ _91455) ^ [] : [-(empty(empty_set))], (377 ^ _91455) ^ [] : [-(function(373 ^ []))], (158 ^ _91455) ^ [_96398, _96400] : [in(_96400, _96398), in(_96398, _96400)], (381 ^ _91455) ^ [] : [-(empty(373 ^ []))], (440 ^ _91455) ^ [_105305, _105307] : [ordinal(_105305), in(_105307, _105305), -(ordinal(_105307))], (484 ^ _91455) ^ [_106632, _106634] : [subset(_106634, _106632), -(element(_106634, powerset(_106632)))], (500 ^ _91455) ^ [_107189, _107191, _107193] : [in(_107193, _107191), element(_107191, powerset(_107189)), empty(_107189)], (263 ^ _91455) ^ [_99634] : [266 ^ _91455 : [(269 ^ _91455) ^ [] : [-(in(265 ^ [_99634], _99634))], (271 ^ _91455) ^ [] : [in(264 ^ [_99634], 265 ^ [_99634])], (273 ^ _91455) ^ [] : [264 ^ [_99634] = 265 ^ [_99634]], (275 ^ _91455) ^ [] : [in(265 ^ [_99634], 264 ^ [_99634])], (267 ^ _91455) ^ [] : [-(in(264 ^ [_99634], _99634))]], -(epsilon_connected(_99634))], (70 ^ _91455) ^ [_93678, _93680] : [-(relation_non_empty(_93678)), _93680 = _93678, relation_non_empty(_93680)], (407 ^ _91455) ^ [] : [-(epsilon_transitive(403 ^ []))], (339 ^ _91455) ^ [] : [-(epsilon_connected(empty_set))], (80 ^ _91455) ^ [_93973, _93975] : [-(function(_93973)), _93975 = _93973, function(_93975)], (423 ^ _91455) ^ [] : [-(function(417 ^ []))], (362 ^ _91455) ^ [] : [-(relation(358 ^ []))], (329 ^ _91455) ^ [] : [-(relation_empty_yielding(empty_set))], (212 ^ _91455) ^ [_97986] : [empty(_97986), 215 ^ _91455 : [(220 ^ _91455) ^ [] : [-(ordinal(_97986))], (218 ^ _91455) ^ [] : [-(epsilon_connected(_97986))], (216 ^ _91455) ^ [] : [-(epsilon_transitive(_97986))]]], (142 ^ _91455) ^ [_95875, _95877] : [-(ordinal(_95875)), _95877 = _95875, ordinal(_95877)], (306 ^ _91455) ^ [_101292] : [-(ordinal(_101292)), epsilon_transitive(_101292), epsilon_connected(_101292)], (317 ^ _91455) ^ [_101587] : [-(element(315 ^ [_101587], _101587))], (30 ^ _91455) ^ [_92498, _92500] : [-(epsilon_transitive(_92498)), _92500 = _92498, epsilon_transitive(_92500)], (390 ^ _91455) ^ [] : [empty(388 ^ [])], (421 ^ _91455) ^ [] : [-(relation_empty_yielding(417 ^ []))], (414 ^ _91455) ^ [] : [-(relation(412 ^ []))], (416 ^ _91455) ^ [] : [-(relation_empty_yielding(412 ^ []))], (241 ^ _91455) ^ [_98996] : [epsilon_connected(_98996), 244 ^ _91455 : [(245 ^ _91455) ^ [_99172, _99174] : [in(_99174, _98996), in(_99172, _98996), -(in(_99174, _99172)), -(_99174 = _99172), -(in(_99172, _99174))]]], (372 ^ _91455) ^ [] : [-(function(366 ^ []))], (350 ^ _91455) ^ [] : [-(function(346 ^ []))], (385 ^ _91455) ^ [] : [-(epsilon_connected(373 ^ []))], (2 ^ _91455) ^ [_91579] : [-(_91579 = _91579)], (468 ^ _91455) ^ [_106139, _106141] : [element(_106141, _106139), -(empty(_106139)), -(in(_106141, _106139))], (333 ^ _91455) ^ [] : [-(one_to_one(empty_set))], (20 ^ _91455) ^ [_92203, _92205] : [-(one_to_one(_92203)), _92205 = _92203, one_to_one(_92205)], (419 ^ _91455) ^ [] : [-(relation(417 ^ []))], (375 ^ _91455) ^ [] : [-(relation(373 ^ []))], (327 ^ _91455) ^ [] : [-(relation(empty_set))], (522 ^ _91455) ^ [_107874, _107876] : [empty(_107876), -(_107876 = _107874), empty(_107874)], (222 ^ _91455) ^ [_98342] : [epsilon_transitive(_98342), 225 ^ _91455 : [(226 ^ _91455) ^ [_98473] : [in(_98473, _98342), -(subset(_98473, _98342))]]], (405 ^ _91455) ^ [] : [empty(403 ^ [])], (40 ^ _91455) ^ [_92793, _92795] : [-(epsilon_connected(_92793)), _92795 = _92793, epsilon_connected(_92795)], (348 ^ _91455) ^ [] : [-(relation(346 ^ []))], (323 ^ _91455) ^ [] : [-(relation_empty_yielding(empty_set))], (178 ^ _91455) ^ [_97038] : [empty(_97038), -(relation(_97038))], (430 ^ _91455) ^ [] : [-(function(424 ^ []))], (478 ^ _91455) ^ [_106466, _106468] : [element(_106468, powerset(_106466)), -(subset(_106468, _106466))], (398 ^ _91455) ^ [] : [-(relation(396 ^ []))], (402 ^ _91455) ^ [] : [-(one_to_one(396 ^ []))], (428 ^ _91455) ^ [] : [-(relation_non_empty(424 ^ []))], (450 ^ _91455) ^ [_105586] : [ordinal(_105586), 453 ^ _91455 : [(454 ^ _91455) ^ [_105736] : [ordinal(_105736), -(in(_105586, _105736)), -(_105586 = _105736), -(in(_105736, _105586))]]], (432 ^ _91455) ^ [_104986, _104988] : [-(subset(_104988, _104988))], (319 ^ _91455) ^ [] : [-(empty(empty_set))], (341 ^ _91455) ^ [] : [-(ordinal(empty_set))], (128 ^ _91455) ^ [_95479, _95481, _95483, _95485] : [-(in(_95483, _95479)), in(_95485, _95481), _95485 = _95483, _95481 = _95479], (383 ^ _91455) ^ [] : [-(epsilon_transitive(373 ^ []))], (360 ^ _91455) ^ [] : [-(empty(358 ^ []))], (387 ^ _91455) ^ [] : [-(ordinal(373 ^ []))], (510 ^ _91455) ^ [_107485] : [empty(_107485), -(_107485 = empty_set)], (490 ^ _91455) ^ [_106862, _106864, _106866] : [-(element(_106866, _106862)), in(_106866, _106864), element(_106864, powerset(_106862))], (202 ^ _91455) ^ [_97717] : [-(ordinal(_97717)), epsilon_transitive(_97717), epsilon_connected(_97717)], (118 ^ _91455) ^ [_95156, _95158] : [-(empty(_95156)), _95158 = _95156, empty(_95158)], (104 ^ _91455) ^ [_94740, _94742, _94744, _94746] : [-(element(_94744, _94740)), element(_94746, _94742), _94746 = _94744, _94742 = _94740], (379 ^ _91455) ^ [] : [-(one_to_one(373 ^ []))], (392 ^ _91455) ^ [] : [-(relation(388 ^ []))]], input).
% 198.90/192.56  ncf('1',plain,[ordinal(233 ^ [531 ^ []]), -(in(233 ^ [531 ^ []], 531 ^ []))],start(539 ^ 0,bind([[_108607], [233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1',plain,[-(ordinal(233 ^ [531 ^ []])), in(233 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 1,bind([[_108453], [233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1',plain,[-(in(233 ^ [531 ^ []], 531 ^ [])), -(epsilon_transitive(531 ^ []))],extension(232 ^ 2,bind([[_98642], [531 ^ []]]))).
% 198.90/192.56  ncf('1.1.1.1',plain,[epsilon_transitive(531 ^ []), -(ordinal(531 ^ [])), epsilon_connected(531 ^ [])],extension(306 ^ 3,bind([[_101292], [531 ^ []]]))).
% 198.90/192.56  ncf('1.1.1.1.1',plain,[ordinal(531 ^ []), -(in(531 ^ [], 531 ^ []))],extension(539 ^ 4,bind([[_108607], [531 ^ []]]))).
% 198.90/192.56  ncf('1.1.1.1.1.1',plain,[in(531 ^ [], 531 ^ []), in(531 ^ [], 531 ^ [])],extension(158 ^ 5,bind([[_96398, _96400], [531 ^ [], 531 ^ []]]))).
% 198.90/192.56  ncf('1.1.1.1.1.1.1',plain,[-(in(531 ^ [], 531 ^ []))],reduction('1.1.1.1.1')).
% 198.90/192.56  ncf('1.1.1.1.2',plain,[-(epsilon_connected(531 ^ [])), 271 : in(264 ^ [531 ^ []], 265 ^ [531 ^ []])],extension(263 ^ 4,bind([[_99634], [531 ^ []]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1',plain,[-(in(264 ^ [531 ^ []], 265 ^ [531 ^ []])), 454 : ordinal(265 ^ [531 ^ []]), 454 : -(264 ^ [531 ^ []] = 265 ^ [531 ^ []]), 454 : -(in(265 ^ [531 ^ []], 264 ^ [531 ^ []])), 454 : ordinal(264 ^ [531 ^ []])],extension(450 ^ 7,bind([[_105586, _105736], [264 ^ [531 ^ []], 265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1.1',plain,[-(ordinal(265 ^ [531 ^ []])), in(265 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 10,bind([[_108453], [265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1.1.1',plain,[-(in(265 ^ [531 ^ []], 531 ^ []))],extension(269 ^ 11)).
% 198.90/192.56  ncf('1.1.1.1.2.1.2',plain,[264 ^ [531 ^ []] = 265 ^ [531 ^ []], -(264 ^ [531 ^ []] = 265 ^ [531 ^ []]), 265 ^ [531 ^ []] = 265 ^ [531 ^ []]],extension(10 ^ 10,bind([[_91890, _91892, _91894], [265 ^ [531 ^ []], 265 ^ [531 ^ []], 264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1.2.1',plain,[264 ^ [531 ^ []] = 265 ^ [531 ^ []]],extension(273 ^ 11)).
% 198.90/192.56  ncf('1.1.1.1.2.1.2.2',plain,[-(265 ^ [531 ^ []] = 265 ^ [531 ^ []])],extension(2 ^ 11,bind([[_91579], [265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1.3',plain,[in(265 ^ [531 ^ []], 264 ^ [531 ^ []])],extension(275 ^ 10)).
% 198.90/192.56  ncf('1.1.1.1.2.1.4',plain,[-(ordinal(264 ^ [531 ^ []])), in(264 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 8,bind([[_108453], [264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.1.1.1.2.1.4.1',plain,[-(in(264 ^ [531 ^ []], 531 ^ []))],extension(267 ^ 9)).
% 198.90/192.56  ncf('1.2',plain,[in(233 ^ [531 ^ []], 531 ^ []), ordinal(531 ^ []), -(ordinal(233 ^ [531 ^ []]))],extension(440 ^ 1,bind([[_105305, _105307], [531 ^ [], 233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1',plain,[-(ordinal(531 ^ [])), epsilon_transitive(531 ^ []), epsilon_connected(531 ^ [])],extension(306 ^ 2,bind([[_101292], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.1.1',plain,[-(epsilon_transitive(531 ^ [])), 237 : subset(233 ^ [531 ^ []], 531 ^ [])],extension(232 ^ 3,bind([[_98642], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.1.1.1',plain,[-(subset(233 ^ [531 ^ []], 531 ^ [])), 294 : in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ [])],extension(289 ^ 6,bind([[_100697, _100699], [531 ^ [], 233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.1.1.1',plain,[-(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ [])), ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]])],extension(539 ^ 9,bind([[_108607], [290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.1.1.1.1.1',plain,[-(ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]])), ordinal(233 ^ [531 ^ []]), in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 233 ^ [531 ^ []])],extension(440 ^ 10,bind([[_105305, _105307], [233 ^ [531 ^ []], 290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.1.1.1.1.1.1',plain,[-(ordinal(233 ^ [531 ^ []])), in(233 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 11,bind([[_108453], [233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.1.1.1.1.1.1',plain,[-(in(233 ^ [531 ^ []], 531 ^ []))],reduction('1')).
% 198.90/192.56  ncf('1.2.1.1.1.1.1.2',plain,[-(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 233 ^ [531 ^ []]))],extension(292 ^ 11)).
% 198.90/192.56  ncf('1.2.1.2',plain,[-(epsilon_connected(531 ^ [])), 271 : in(264 ^ [531 ^ []], 265 ^ [531 ^ []])],extension(263 ^ 3,bind([[_99634], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.1.2.1',plain,[-(in(264 ^ [531 ^ []], 265 ^ [531 ^ []])), 454 : ordinal(265 ^ [531 ^ []]), 454 : -(264 ^ [531 ^ []] = 265 ^ [531 ^ []]), 454 : -(in(265 ^ [531 ^ []], 264 ^ [531 ^ []])), 454 : ordinal(264 ^ [531 ^ []])],extension(450 ^ 6,bind([[_105586, _105736], [264 ^ [531 ^ []], 265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.1',plain,[-(ordinal(265 ^ [531 ^ []])), in(265 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 9,bind([[_108453], [265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.1.1',plain,[-(in(265 ^ [531 ^ []], 531 ^ [])), 283 : in(265 ^ [531 ^ []], 531 ^ []), 283 : subset(531 ^ [], 531 ^ [])],extension(279 ^ 10,bind([[_100383, _100385, _100520], [531 ^ [], 531 ^ [], 265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.1.1.1',plain,[-(in(265 ^ [531 ^ []], 531 ^ []))],extension(269 ^ 13)).
% 198.90/192.56  ncf('1.2.1.2.1.1.1.2',plain,[-(subset(531 ^ [], 531 ^ []))],extension(432 ^ 11,bind([[_104986, _104988], [_66889, 531 ^ []]]))).
% 198.90/192.56  ncf('1.2.1.2.1.2',plain,[264 ^ [531 ^ []] = 265 ^ [531 ^ []], -(264 ^ [531 ^ []] = 264 ^ [531 ^ []]), 265 ^ [531 ^ []] = 264 ^ [531 ^ []]],extension(10 ^ 9,bind([[_91890, _91892, _91894], [264 ^ [531 ^ []], 265 ^ [531 ^ []], 264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.2.1',plain,[264 ^ [531 ^ []] = 264 ^ [531 ^ []], -(264 ^ [531 ^ []] = 265 ^ [531 ^ []]), 264 ^ [531 ^ []] = 265 ^ [531 ^ []]],extension(10 ^ 10,bind([[_91890, _91892, _91894], [265 ^ [531 ^ []], 264 ^ [531 ^ []], 264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.2.1.1',plain,[264 ^ [531 ^ []] = 265 ^ [531 ^ []]],extension(273 ^ 11)).
% 198.90/192.56  ncf('1.2.1.2.1.2.1.2',plain,[-(264 ^ [531 ^ []] = 265 ^ [531 ^ []])],reduction('1.2.1.2.1')).
% 198.90/192.56  ncf('1.2.1.2.1.2.2',plain,[-(265 ^ [531 ^ []] = 264 ^ [531 ^ []]), 265 ^ [531 ^ []] = 264 ^ [531 ^ []], 264 ^ [531 ^ []] = 264 ^ [531 ^ []]],extension(10 ^ 10,bind([[_91890, _91892, _91894], [264 ^ [531 ^ []], 264 ^ [531 ^ []], 265 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.2.2.1',plain,[-(265 ^ [531 ^ []] = 264 ^ [531 ^ []]), 264 ^ [531 ^ []] = 265 ^ [531 ^ []]],extension(4 ^ 11,bind([[_91686, _91688], [265 ^ [531 ^ []], 264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.2.2.1.1',plain,[-(264 ^ [531 ^ []] = 265 ^ [531 ^ []])],reduction('1.2.1.2.1')).
% 198.90/192.56  ncf('1.2.1.2.1.2.2.2',plain,[-(264 ^ [531 ^ []] = 264 ^ [531 ^ []])],extension(2 ^ 11,bind([[_91579], [264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.3',plain,[in(265 ^ [531 ^ []], 264 ^ [531 ^ []])],extension(275 ^ 9)).
% 198.90/192.56  ncf('1.2.1.2.1.4',plain,[-(ordinal(264 ^ [531 ^ []])), in(264 ^ [531 ^ []], 531 ^ [])],extension(533 ^ 7,bind([[_108453], [264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.4.1',plain,[-(in(264 ^ [531 ^ []], 531 ^ [])), 283 : in(264 ^ [531 ^ []], 531 ^ []), 283 : subset(531 ^ [], 531 ^ [])],extension(279 ^ 8,bind([[_100383, _100385, _100520], [531 ^ [], 531 ^ [], 264 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.1.2.1.4.1.1',plain,[-(in(264 ^ [531 ^ []], 531 ^ []))],extension(267 ^ 11)).
% 198.90/192.56  ncf('1.2.1.2.1.4.1.2',plain,[-(subset(531 ^ [], 531 ^ []))],extension(432 ^ 9,bind([[_104986, _104988], [_70007, 531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2',plain,[ordinal(233 ^ [531 ^ []]), in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 233 ^ [531 ^ []]), -(ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]]))],extension(440 ^ 2,bind([[_105305, _105307], [233 ^ [531 ^ []], 290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.2.1',plain,[-(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 233 ^ [531 ^ []])), -(subset(233 ^ [531 ^ []], 531 ^ []))],extension(289 ^ 3,bind([[_100697, _100699], [531 ^ [], 233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.2.1.1',plain,[subset(233 ^ [531 ^ []], 531 ^ []), -(epsilon_transitive(531 ^ []))],extension(232 ^ 4,bind([[_98642], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.1.1.1',plain,[epsilon_transitive(531 ^ []), -(ordinal(531 ^ [])), epsilon_connected(531 ^ [])],extension(306 ^ 5,bind([[_101292], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.1.1.1.1',plain,[ordinal(531 ^ []), -(in(531 ^ [], 531 ^ []))],extension(539 ^ 6,bind([[_108607], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.1.1.1.1.1',plain,[in(531 ^ [], 531 ^ []), in(531 ^ [], 531 ^ [])],extension(158 ^ 7,bind([[_96398, _96400], [531 ^ [], 531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.1.1.1.1.1.1',plain,[-(in(531 ^ [], 531 ^ []))],reduction('1.2.2.1.1.1.1')).
% 198.90/192.56  ncf('1.2.2.1.1.1.2',plain,[-(epsilon_connected(531 ^ [])), ordinal(531 ^ [])],extension(298 ^ 6,bind([[_101069], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.1.1.1.2.1',plain,[-(ordinal(531 ^ []))],lemmata('[1].x')).
% 198.90/192.56  ncf('1.2.2.2',plain,[ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]]), 302 : -(epsilon_transitive(290 ^ [531 ^ [], 233 ^ [531 ^ []]]))],extension(298 ^ 3,bind([[_101069], [290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.2.2.1',plain,[epsilon_transitive(290 ^ [531 ^ [], 233 ^ [531 ^ []]]), -(epsilon_transitive(531 ^ [])), 290 ^ [531 ^ [], 233 ^ [531 ^ []]] = 531 ^ []],extension(30 ^ 6,bind([[_92498, _92500], [531 ^ [], 290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.2.2.1.1',plain,[epsilon_transitive(531 ^ []), -(ordinal(531 ^ [])), epsilon_connected(531 ^ [])],extension(306 ^ 7,bind([[_101292], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.1.1',plain,[ordinal(531 ^ []), -(in(531 ^ [], 531 ^ []))],extension(539 ^ 8,bind([[_108607], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.1.1.1',plain,[in(531 ^ [], 531 ^ []), in(531 ^ [], 531 ^ [])],extension(158 ^ 9,bind([[_96398, _96400], [531 ^ [], 531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.1.1.1.1',plain,[-(in(531 ^ [], 531 ^ []))],reduction('1.2.2.2.1.1.1')).
% 198.90/192.56  ncf('1.2.2.2.1.1.2',plain,[-(epsilon_connected(531 ^ [])), ordinal(531 ^ [])],extension(298 ^ 8,bind([[_101069], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.1.2.1',plain,[-(ordinal(531 ^ []))],lemmata('[1].x')).
% 198.90/192.56  ncf('1.2.2.2.1.2',plain,[-(290 ^ [531 ^ [], 233 ^ [531 ^ []]] = 531 ^ []), 245 : in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ []), 245 : in(531 ^ [], 531 ^ []), 245 : -(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ [])), 245 : -(in(531 ^ [], 290 ^ [531 ^ [], 233 ^ [531 ^ []]])), 245 : epsilon_connected(531 ^ [])],extension(241 ^ 7,bind([[_98996, _99172, _99174], [531 ^ [], 531 ^ [], 290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.1',plain,[-(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ [])), ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]])],extension(539 ^ 10,bind([[_108607], [290 ^ [531 ^ [], 233 ^ [531 ^ []]]]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.1.1',plain,[-(ordinal(290 ^ [531 ^ [], 233 ^ [531 ^ []]]))],reduction('1.2.2')).
% 198.90/192.56  ncf('1.2.2.2.1.2.2',plain,[-(in(531 ^ [], 531 ^ [])), ordinal(531 ^ [])],extension(539 ^ 10,bind([[_108607], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.2.1',plain,[-(ordinal(531 ^ []))],lemmata('[1].x')).
% 198.90/192.56  ncf('1.2.2.2.1.2.3',plain,[in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ []), -(subset(233 ^ [531 ^ []], 531 ^ []))],extension(289 ^ 10,bind([[_100697, _100699], [531 ^ [], 233 ^ [531 ^ []]]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.3.1',plain,[subset(233 ^ [531 ^ []], 531 ^ []), -(epsilon_transitive(531 ^ []))],extension(232 ^ 11,bind([[_98642], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.3.1.1',plain,[epsilon_transitive(531 ^ [])],lemmata('[2, 2, 2, 1].x')).
% 198.90/192.56  ncf('1.2.2.2.1.2.4',plain,[in(531 ^ [], 290 ^ [531 ^ [], 233 ^ [531 ^ []]]), in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ [])],extension(158 ^ 10,bind([[_96398, _96400], [290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.4.1',plain,[-(in(290 ^ [531 ^ [], 233 ^ [531 ^ []]], 531 ^ []))],lemmata('[1, 2, 2, 2, 1].x')).
% 198.90/192.56  ncf('1.2.2.2.1.2.5',plain,[-(epsilon_connected(531 ^ [])), ordinal(531 ^ [])],extension(298 ^ 8,bind([[_101069], [531 ^ []]]))).
% 198.90/192.56  ncf('1.2.2.2.1.2.5.1',plain,[-(ordinal(531 ^ []))],lemmata('[1].x')).
% 198.90/192.56  %-----------------------------------------------------
% 198.90/192.56  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------