%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU238+3 : TPTP v8.1.2. Released 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 12:02:49 EDT 2023

% Result   : Theorem 46.78s 45.95s
% Output   : Proof 46.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU238+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 12:54:32 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 46.78/45.95  
% 46.78/45.95  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 46.78/45.95  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.78/45.95  %-----------------------------------------------------
% 46.78/45.95  ncf(matrix, plain, [(652 ^ _136019) ^ [] : [662 ^ _136019 : [(667 ^ _136019) ^ [] : [-(being_limit_ordinal(648 ^ []))], (665 ^ _136019) ^ [] : [-(648 ^ [] = succ(661 ^ []))], (663 ^ _136019) ^ [] : [-(ordinal(661 ^ []))]], 653 ^ _136019 : [(656 ^ _136019) ^ [_136213] : [ordinal(_136213), 648 ^ [] = succ(_136213)], (654 ^ _136019) ^ [] : [being_limit_ordinal(648 ^ [])]]], (650 ^ _136019) ^ [] : [-(ordinal(648 ^ []))], !, (471 ^ _115410) ^ [] : [-(function(465 ^ []))], (4 ^ _115410) ^ [_115641, _115643] : [_115643 = _115641, -(_115641 = _115643)], (236 ^ _115410) ^ [_122975] : [ordinal(_122975), 239 ^ _115410 : [(242 ^ _115410) ^ [] : [-(epsilon_connected(_122975))], (240 ^ _115410) ^ [] : [-(epsilon_transitive(_122975))]]], (410 ^ _115410) ^ [] : [-(relation(406 ^ []))], (403 ^ _115410) ^ [] : [-(epsilon_connected(399 ^ []))], (20 ^ _115410) ^ [_116158, _116160] : [-(one_to_one(_116158)), _116160 = _116158, one_to_one(_116160)], (459 ^ _115410) ^ [] : [-(ordinal(451 ^ []))], (455 ^ _115410) ^ [] : [-(epsilon_transitive(451 ^ []))], (438 ^ _115410) ^ [] : [empty(436 ^ [])], (212 ^ _115410) ^ [_122117, _122119] : [_122119 = _122117, -(succ(_122119) = succ(_122117))], (341 ^ _115410) ^ [] : [-(function(empty_set))], (268 ^ _115410) ^ [_123911] : [-(ordinal(_123911)), epsilon_transitive(_123911), epsilon_connected(_123911)], (393 ^ _115410) ^ [_127852, _127854] : [proper_subset(_127854, _127854)], (345 ^ _115410) ^ [] : [-(empty(empty_set))], (450 ^ _115410) ^ [] : [-(one_to_one(444 ^ []))], (435 ^ _115410) ^ [] : [-(ordinal(421 ^ []))], (440 ^ _115410) ^ [] : [-(relation(436 ^ []))], (349 ^ _115410) ^ [] : [-(epsilon_connected(empty_set))], (425 ^ _115410) ^ [] : [-(function(421 ^ []))], (244 ^ _115410) ^ [_123232] : [empty(_123232), -(relation(_123232))], (427 ^ _115410) ^ [] : [-(one_to_one(421 ^ []))], (512 ^ _115410) ^ [_131408] : [-(in(_131408, succ(_131408)))], (206 ^ _115410) ^ [_121919, _121921] : [_121921 = _121919, -(powerset(_121921) = powerset(_121919))], (423 ^ _115410) ^ [] : [-(relation(421 ^ []))], (408 ^ _115410) ^ [] : [-(empty(406 ^ []))], (218 ^ _115410) ^ [_122381, _122383] : [in(_122383, _122381), in(_122381, _122383)], (578 ^ _115410) ^ [_133524] : [ordinal(_133524), 581 ^ _115410 : [(582 ^ _115410) ^ [] : [being_limit_ordinal(_133524), 585 ^ _115410 : [(586 ^ _115410) ^ [_133770] : [ordinal(_133770), in(_133770, _133524), -(in(succ(_133770), _133524))]]], (596 ^ _115410) ^ [] : [598 ^ _115410 : [(603 ^ _115410) ^ [] : [in(succ(597 ^ [_133524]), _133524)], (601 ^ _115410) ^ [] : [-(in(597 ^ [_133524], _133524))], (599 ^ _115410) ^ [] : [-(ordinal(597 ^ [_133524]))]], -(being_limit_ordinal(_133524))]]], (196 ^ _115410) ^ [_121588, _121590, _121592, _121594] : [-(set_union2(_121594, _121590) = set_union2(_121592, _121588)), _121594 = _121592, _121590 = _121588], (304 ^ _115410) ^ [_124979] : [-(succ(_124979) = set_union2(_124979, singleton(_124979)))], (118 ^ _115410) ^ [_119139, _119141, _119143, _119145] : [-(subset(_119143, _119139)), subset(_119145, _119141), _119145 = _119143, _119141 = _119139], (180 ^ _115410) ^ [_121013, _121015] : [-(being_limit_ordinal(_121013)), _121015 = _121013, being_limit_ordinal(_121015)], (420 ^ _115410) ^ [] : [-(function(414 ^ []))], (50 ^ _115410) ^ [_117043, _117045] : [-(relation(_117043)), _117045 = _117043, relation(_117045)], (457 ^ _115410) ^ [] : [-(epsilon_connected(451 ^ []))], (474 ^ _115410) ^ [] : [-(relation(472 ^ []))], (306 ^ _115410) ^ [_125122, _125124] : [proper_subset(_125124, _125122), 309 ^ _115410 : [(312 ^ _115410) ^ [] : [_125124 = _125122], (310 ^ _115410) ^ [] : [-(subset(_125124, _125122))]]], (433 ^ _115410) ^ [] : [-(epsilon_connected(421 ^ []))], (446 ^ _115410) ^ [] : [-(relation(444 ^ []))], (389 ^ _115410) ^ [] : [-(relation(empty_set))], (325 ^ _115410) ^ [_125674] : [-(element(323 ^ [_125674], _125674))], (170 ^ _115410) ^ [_120738, _120740] : [-(ordinal(_120738)), _120740 = _120738, ordinal(_120740)], (401 ^ _115410) ^ [] : [-(epsilon_transitive(399 ^ []))], (398 ^ _115410) ^ [] : [-(function(394 ^ []))], (510 ^ _115410) ^ [_131328, _131330] : [-(subset(_131330, _131330))], (478 ^ _115410) ^ [] : [-(function(472 ^ []))], (639 ^ _115410) ^ [_135436, _135438] : [empty(_135438), -(_135438 = _135436), empty(_135436)], (453 ^ _115410) ^ [] : [empty(451 ^ [])], (60 ^ _115410) ^ [_117338, _117340] : [-(relation_non_empty(_117338)), _117340 = _117338, relation_non_empty(_117340)], (80 ^ _115410) ^ [_117928, _117930] : [-(epsilon_transitive(_117928)), _117930 = _117928, epsilon_transitive(_117930)], (443 ^ _115410) ^ [] : [empty(441 ^ [])], (327 ^ _115410) ^ [] : [-(empty(empty_set))], (343 ^ _115410) ^ [] : [-(one_to_one(empty_set))], (448 ^ _115410) ^ [] : [-(function(444 ^ []))], (290 ^ _115410) ^ [_124621, _124623] : [ordinal(_124623), ordinal(_124621), -(ordinal_subset(_124623, _124621)), -(ordinal_subset(_124621, _124623))], (572 ^ _115410) ^ [_133322, _133324] : [subset(_133324, _133322), -(element(_133324, powerset(_133322)))], (514 ^ _115410) ^ [_131488] : [-(set_union2(_131488, empty_set) = _131488)], (522 ^ _115410) ^ [_131794] : [epsilon_transitive(_131794), 525 ^ _115410 : [(526 ^ _115410) ^ [_131930] : [ordinal(_131930), proper_subset(_131794, _131930), -(in(_131794, _131930))]]], (104 ^ _115410) ^ [_118695, _118697, _118699, _118701] : [-(ordinal_subset(_118699, _118695)), ordinal_subset(_118701, _118697), _118701 = _118699, _118697 = _118695], (480 ^ _115410) ^ [_130501, _130503] : [ordinal(_130503), ordinal(_130501), 487 ^ _115410 : [(494 ^ _115410) ^ [] : [subset(_130503, _130501), -(ordinal_subset(_130503, _130501))], (488 ^ _115410) ^ [] : [ordinal_subset(_130503, _130501), -(subset(_130503, _130501))]]], (633 ^ _115410) ^ [_135249, _135251] : [in(_135251, _135249), empty(_135249)], (396 ^ _115410) ^ [] : [-(relation(394 ^ []))], (429 ^ _115410) ^ [] : [-(empty(421 ^ []))], (339 ^ _115410) ^ [] : [-(relation_empty_yielding(empty_set))], (10 ^ _115410) ^ [_115845, _115847, _115849] : [-(_115849 = _115845), _115849 = _115847, _115847 = _115845], (347 ^ _115410) ^ [] : [-(epsilon_transitive(empty_set))], (30 ^ _115410) ^ [_116453, _116455] : [-(epsilon_connected(_116453)), _116455 = _116453, epsilon_connected(_116455)], (536 ^ _115410) ^ [_132234, _132236] : [element(_132236, _132234), -(empty(_132234)), -(in(_132236, _132234))], (627 ^ _115410) ^ [_135047] : [empty(_135047), -(_135047 = empty_set)], (314 ^ _115410) ^ [_125360, _125362] : [-(proper_subset(_125362, _125360)), subset(_125362, _125360), -(_125362 = _125360)], (40 ^ _115410) ^ [_116748, _116750] : [-(relation_empty_yielding(_116748)), _116750 = _116748, relation_empty_yielding(_116750)], (331 ^ _115410) ^ [] : [-(relation_empty_yielding(empty_set))], (230 ^ _115410) ^ [_122789] : [empty(_122789), -(function(_122789))], (467 ^ _115410) ^ [] : [-(relation(465 ^ []))], (132 ^ _115410) ^ [_119583, _119585, _119587, _119589] : [-(element(_119587, _119583)), element(_119589, _119585), _119589 = _119587, _119585 = _119583], (405 ^ _115410) ^ [] : [-(ordinal(399 ^ []))], (369 ^ _115410) ^ [_127019] : [ordinal(_127019), 372 ^ _115410 : [(375 ^ _115410) ^ [] : [-(epsilon_transitive(succ(_127019)))], (377 ^ _115410) ^ [] : [-(epsilon_connected(succ(_127019)))], (379 ^ _115410) ^ [] : [-(ordinal(succ(_127019)))], (373 ^ _115410) ^ [] : [empty(succ(_127019))]]], (353 ^ _115410) ^ [_126518, _126520] : [-(relation(set_union2(_126520, _126518))), relation(_126520), relation(_126518)], (476 ^ _115410) ^ [] : [-(relation_non_empty(472 ^ []))], (381 ^ _115410) ^ [_127447, _127449] : [-(empty(_127449)), empty(set_union2(_127447, _127449))], (146 ^ _115410) ^ [_120027, _120029, _120031, _120033] : [-(in(_120031, _120027)), in(_120033, _120029), _120033 = _120031, _120029 = _120027], (413 ^ _115410) ^ [] : [-(empty(411 ^ []))], (288 ^ _115410) ^ [_124506, _124508] : [-(set_union2(_124508, _124506) = set_union2(_124506, _124508))], (190 ^ _115410) ^ [_121342, _121344] : [_121344 = _121342, -(singleton(_121344) = singleton(_121342))], (351 ^ _115410) ^ [] : [-(ordinal(empty_set))], (335 ^ _115410) ^ [] : [-(empty(empty_set))], (329 ^ _115410) ^ [] : [-(relation(empty_set))], (431 ^ _115410) ^ [] : [-(epsilon_transitive(421 ^ []))], (224 ^ _115410) ^ [_122592, _122594] : [proper_subset(_122594, _122592), proper_subset(_122592, _122594)], (250 ^ _115410) ^ [_123418] : [261 ^ _115410 : [(266 ^ _115410) ^ [] : [-(one_to_one(_123418))], (264 ^ _115410) ^ [] : [-(function(_123418))], (262 ^ _115410) ^ [] : [-(relation(_123418))]], relation(_123418), empty(_123418), function(_123418)], (566 ^ _115410) ^ [_133156, _133158] : [element(_133158, powerset(_133156)), -(subset(_133158, _133156))], (607 ^ _115410) ^ [_134424, _134426, _134428] : [-(element(_134428, _134424)), in(_134428, _134426), element(_134426, powerset(_134424))], (469 ^ _115410) ^ [] : [-(relation_empty_yielding(465 ^ []))], (546 ^ _115410) ^ [_132518] : [ordinal(_132518), 549 ^ _115410 : [(550 ^ _115410) ^ [_132656] : [ordinal(_132656), 553 ^ _115410 : [(560 ^ _115410) ^ [] : [ordinal_subset(succ(_132518), _132656), -(in(_132518, _132656))], (554 ^ _115410) ^ [] : [in(_132518, _132656), -(ordinal_subset(succ(_132518), _132656))]]]]], (333 ^ _115410) ^ [_125919] : [empty(succ(_125919))], (278 ^ _115410) ^ [_124180] : [empty(_124180), 281 ^ _115410 : [(286 ^ _115410) ^ [] : [-(ordinal(_124180))], (284 ^ _115410) ^ [] : [-(epsilon_connected(_124180))], (282 ^ _115410) ^ [] : [-(epsilon_transitive(_124180))]]], (391 ^ _115410) ^ [_127756, _127758] : [-(set_union2(_127758, _127758) = _127758)], (337 ^ _115410) ^ [] : [-(relation(empty_set))], (90 ^ _115410) ^ [_118251, _118253, _118255, _118257] : [-(proper_subset(_118255, _118251)), proper_subset(_118257, _118253), _118257 = _118255, _118253 = _118251], (462 ^ _115410) ^ [] : [-(relation(460 ^ []))], (500 ^ _115410) ^ [_131048, _131050] : [-(ordinal_subset(_131050, _131050)), ordinal(_131050), ordinal(_131048)], (160 ^ _115410) ^ [_120443, _120445] : [-(empty(_120443)), _120445 = _120443, empty(_120445)], (464 ^ _115410) ^ [] : [-(relation_empty_yielding(460 ^ []))], (617 ^ _115410) ^ [_134751, _134753, _134755] : [in(_134755, _134753), element(_134753, powerset(_134751)), empty(_134751)], (70 ^ _115410) ^ [_117633, _117635] : [-(function(_117633)), _117635 = _117633, function(_117635)], (418 ^ _115410) ^ [] : [-(empty(414 ^ []))], (416 ^ _115410) ^ [] : [-(relation(414 ^ []))], (2 ^ _115410) ^ [_115534] : [-(_115534 = _115534)], (387 ^ _115410) ^ [] : [-(empty(empty_set))], (363 ^ _115410) ^ [_126817, _126819] : [-(empty(_126819)), empty(set_union2(_126819, _126817))], (516 ^ _115410) ^ [_131598, _131600] : [in(_131600, _131598), -(element(_131600, _131598))]], input).
% 46.78/45.95  ncf('1',plain,[667 : -(being_limit_ordinal(648 ^ [])), 654 : being_limit_ordinal(648 ^ [])],start(652 ^ 0)).
% 46.78/45.95  ncf('1.1',plain,[being_limit_ordinal(648 ^ []), 586 : ordinal(661 ^ []), 586 : in(661 ^ [], 648 ^ []), 586 : -(in(succ(661 ^ []), 648 ^ [])), 582 : ordinal(648 ^ [])],extension(578 ^ 3,bind([[_133524, _133770], [648 ^ [], 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.1',plain,[-(ordinal(661 ^ []))],extension(663 ^ 8)).
% 46.78/45.95  ncf('1.1.2',plain,[-(in(661 ^ [], 648 ^ [])), element(661 ^ [], 648 ^ []), -(empty(648 ^ []))],extension(536 ^ 8,bind([[_132234, _132236], [648 ^ [], 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.1',plain,[-(element(661 ^ [], 648 ^ [])), in(661 ^ [], succ(661 ^ [])), element(succ(661 ^ []), powerset(648 ^ []))],extension(607 ^ 9,bind([[_134424, _134426, _134428], [648 ^ [], succ(661 ^ []), 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.1.1',plain,[-(in(661 ^ [], succ(661 ^ [])))],extension(512 ^ 10,bind([[_131408], [661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.1.2',plain,[-(element(succ(661 ^ []), powerset(648 ^ []))), subset(succ(661 ^ []), 648 ^ [])],extension(572 ^ 10,bind([[_133322, _133324], [648 ^ [], succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.2.1.2.1',plain,[-(subset(succ(661 ^ []), 648 ^ [])), subset(648 ^ [], 648 ^ []), 648 ^ [] = succ(661 ^ []), 648 ^ [] = 648 ^ []],extension(118 ^ 11,bind([[_119139, _119141, _119143, _119145], [648 ^ [], 648 ^ [], succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.1.2.1.1',plain,[-(subset(648 ^ [], 648 ^ []))],extension(510 ^ 12,bind([[_131328, _131330], [_74872, 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.1.2.1.2',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 12)).
% 46.78/45.95  ncf('1.1.2.1.2.1.3',plain,[-(648 ^ [] = 648 ^ [])],extension(2 ^ 12,bind([[_115534], [648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2',plain,[empty(648 ^ []), -(648 ^ [] = 661 ^ []), empty(661 ^ [])],extension(639 ^ 9,bind([[_135436, _135438], [661 ^ [], 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1',plain,[648 ^ [] = 661 ^ [], -(661 ^ [] = 648 ^ [])],extension(4 ^ 10,bind([[_115641, _115643], [661 ^ [], 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1.1',plain,[661 ^ [] = 648 ^ [], -(ordinal_subset(succ(661 ^ []), 648 ^ [])), ordinal_subset(661 ^ [], 661 ^ []), 661 ^ [] = succ(661 ^ [])],extension(104 ^ 11,bind([[_118695, _118697, _118699, _118701], [648 ^ [], 661 ^ [], succ(661 ^ []), 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1.1.1',plain,[ordinal_subset(succ(661 ^ []), 648 ^ []), 560 : -(in(661 ^ [], 648 ^ [])), 560 : ordinal(648 ^ []), 550 : ordinal(661 ^ [])],extension(546 ^ 12,bind([[_132518, _132656], [661 ^ [], 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1.1.1.1',plain,[in(661 ^ [], 648 ^ [])],reduction('1.1')).
% 46.78/45.95  ncf('1.1.2.2.1.1.1.2',plain,[-(ordinal(648 ^ []))],extension(650 ^ 15)).
% 46.78/45.95  ncf('1.1.2.2.1.1.1.3',plain,[-(ordinal(661 ^ []))],lemmata('[1].x')).
% 46.78/45.95  ncf('1.1.2.2.1.1.2',plain,[-(ordinal_subset(661 ^ [], 661 ^ [])), ordinal(661 ^ []), ordinal(661 ^ []), -(ordinal_subset(661 ^ [], 661 ^ []))],extension(290 ^ 12,bind([[_124621, _124623], [661 ^ [], 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1.1.2.1',plain,[-(ordinal(661 ^ []))],extension(663 ^ 13)).
% 46.78/45.95  ncf('1.1.2.2.1.1.2.2',plain,[-(ordinal(661 ^ []))],extension(663 ^ 13)).
% 46.78/45.95  ncf('1.1.2.2.1.1.2.3',plain,[ordinal_subset(661 ^ [], 661 ^ [])],reduction('1.1.2.2.1.1')).
% 46.78/45.95  ncf('1.1.2.2.1.1.3',plain,[-(661 ^ [] = succ(661 ^ [])), 661 ^ [] = 648 ^ [], 648 ^ [] = succ(661 ^ [])],extension(10 ^ 12,bind([[_115845, _115847, _115849], [succ(661 ^ []), 648 ^ [], 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.1.1.3.1',plain,[-(661 ^ [] = 648 ^ [])],reduction('1.1.2.2.1')).
% 46.78/45.95  ncf('1.1.2.2.1.1.3.2',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 13)).
% 46.78/45.95  ncf('1.1.2.2.2',plain,[-(empty(661 ^ [])), empty(set_union2(661 ^ [], singleton(661 ^ [])))],extension(363 ^ 10,bind([[_126817, _126819], [singleton(661 ^ []), 661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.2.1',plain,[-(empty(set_union2(661 ^ [], singleton(661 ^ [])))), succ(661 ^ []) = set_union2(661 ^ [], singleton(661 ^ [])), empty(succ(661 ^ []))],extension(160 ^ 11,bind([[_120443, _120445], [set_union2(661 ^ [], singleton(661 ^ [])), succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.2.2.2.1.1',plain,[-(succ(661 ^ []) = set_union2(661 ^ [], singleton(661 ^ [])))],extension(304 ^ 12,bind([[_124979], [661 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.2.1.2',plain,[-(empty(succ(661 ^ []))), 648 ^ [] = succ(661 ^ []), empty(648 ^ [])],extension(160 ^ 12,bind([[_120443, _120445], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.2.2.2.1.2.1',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 13)).
% 46.78/45.95  ncf('1.1.2.2.2.1.2.2',plain,[-(empty(648 ^ []))],reduction('1.1.2')).
% 46.78/45.95  ncf('1.1.3',plain,[in(succ(661 ^ []), 648 ^ []), in(648 ^ [], succ(661 ^ []))],extension(218 ^ 8,bind([[_122381, _122383], [648 ^ [], succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1',plain,[-(in(648 ^ [], succ(661 ^ []))), 526 : ordinal(succ(661 ^ [])), 526 : proper_subset(648 ^ [], succ(661 ^ [])), 526 : epsilon_transitive(648 ^ [])],extension(522 ^ 9,bind([[_131794, _131930], [648 ^ [], succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.1',plain,[-(ordinal(succ(661 ^ []))), epsilon_transitive(succ(661 ^ [])), epsilon_connected(succ(661 ^ []))],extension(268 ^ 12,bind([[_123911], [succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.1.1',plain,[-(epsilon_transitive(succ(661 ^ []))), 648 ^ [] = succ(661 ^ []), epsilon_transitive(648 ^ [])],extension(80 ^ 13,bind([[_117928, _117930], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.1.1.1',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 14)).
% 46.78/45.95  ncf('1.1.3.1.1.1.2',plain,[-(epsilon_transitive(648 ^ [])), ordinal(648 ^ [])],extension(236 ^ 14,bind([[_122975], [648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.1.1.2.1',plain,[-(ordinal(648 ^ []))],extension(650 ^ 15)).
% 46.78/45.95  ncf('1.1.3.1.1.2',plain,[-(epsilon_connected(succ(661 ^ []))), 648 ^ [] = succ(661 ^ []), epsilon_connected(648 ^ [])],extension(30 ^ 13,bind([[_116453, _116455], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.1.2.1',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 14)).
% 46.78/45.95  ncf('1.1.3.1.1.2.2',plain,[-(epsilon_connected(648 ^ [])), ordinal(648 ^ [])],extension(236 ^ 14,bind([[_122975], [648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.1.2.2.1',plain,[-(ordinal(648 ^ []))],extension(650 ^ 15)).
% 46.78/45.95  ncf('1.1.3.1.2',plain,[-(proper_subset(648 ^ [], succ(661 ^ []))), subset(648 ^ [], succ(661 ^ [])), -(648 ^ [] = succ(661 ^ []))],extension(314 ^ 12,bind([[_125360, _125362], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.2.1',plain,[-(subset(648 ^ [], succ(661 ^ []))), subset(succ(661 ^ []), succ(661 ^ [])), succ(661 ^ []) = 648 ^ [], succ(661 ^ []) = succ(661 ^ [])],extension(118 ^ 13,bind([[_119139, _119141, _119143, _119145], [succ(661 ^ []), succ(661 ^ []), 648 ^ [], succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.2.1.1',plain,[-(subset(succ(661 ^ []), succ(661 ^ [])))],extension(510 ^ 14,bind([[_131328, _131330], [_84534, succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.2.1.2',plain,[-(succ(661 ^ []) = 648 ^ []), 648 ^ [] = succ(661 ^ [])],extension(4 ^ 14,bind([[_115641, _115643], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.2.1.2.1',plain,[-(648 ^ [] = succ(661 ^ []))],extension(665 ^ 15)).
% 46.78/45.95  ncf('1.1.3.1.2.1.3',plain,[-(succ(661 ^ []) = succ(661 ^ []))],extension(2 ^ 14,bind([[_115534], [succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.2.2',plain,[648 ^ [] = succ(661 ^ []), -(succ(661 ^ []) = 648 ^ [])],extension(4 ^ 13,bind([[_115641, _115643], [succ(661 ^ []), 648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.2.2.1',plain,[succ(661 ^ []) = 648 ^ [], -(in(648 ^ [], succ(661 ^ []))), in(succ(661 ^ []), 648 ^ []), 648 ^ [] = succ(661 ^ [])],extension(146 ^ 14,bind([[_120027, _120029, _120031, _120033], [succ(661 ^ []), 648 ^ [], 648 ^ [], succ(661 ^ [])]]))).
% 46.78/45.95  ncf('1.1.3.1.2.2.1.1',plain,[in(648 ^ [], succ(661 ^ []))],reduction('1.1.3')).
% 46.78/45.95  ncf('1.1.3.1.2.2.1.2',plain,[-(in(succ(661 ^ []), 648 ^ []))],reduction('1.1')).
% 46.78/45.95  ncf('1.1.3.1.2.2.1.3',plain,[-(648 ^ [] = succ(661 ^ []))],reduction('1.1.3.1.2')).
% 46.78/45.95  ncf('1.1.3.1.3',plain,[-(epsilon_transitive(648 ^ [])), ordinal(648 ^ [])],extension(236 ^ 10,bind([[_122975], [648 ^ []]]))).
% 46.78/45.95  ncf('1.1.3.1.3.1',plain,[-(ordinal(648 ^ []))],extension(650 ^ 11)).
% 46.78/45.95  ncf('1.1.4',plain,[-(ordinal(648 ^ []))],extension(650 ^ 4)).
% 46.78/45.95  ncf('1.2',plain,[-(being_limit_ordinal(648 ^ [])), 603 : in(succ(597 ^ [648 ^ []]), 648 ^ []), 596 : ordinal(648 ^ [])],extension(578 ^ 3,bind([[_133524], [648 ^ []]]))).
% 46.78/45.95  ncf('1.2.1',plain,[-(in(succ(597 ^ [648 ^ []]), 648 ^ [])), 526 : ordinal(648 ^ []), 526 : proper_subset(succ(597 ^ [648 ^ []]), 648 ^ []), 526 : epsilon_transitive(succ(597 ^ [648 ^ []]))],extension(522 ^ 8,bind([[_131794, _131930], [succ(597 ^ [648 ^ []]), 648 ^ []]]))).
% 46.78/45.95  ncf('1.2.1.1',plain,[-(ordinal(648 ^ []))],extension(650 ^ 11)).
% 46.78/45.95  ncf('1.2.1.2',plain,[-(proper_subset(succ(597 ^ [648 ^ []]), 648 ^ [])), subset(succ(597 ^ [648 ^ []]), 648 ^ []), -(succ(597 ^ [648 ^ []]) = 648 ^ [])],extension(314 ^ 11,bind([[_125360, _125362], [648 ^ [], succ(597 ^ [648 ^ []])]]))).
% 46.78/45.95  ncf('1.2.1.2.1',plain,[-(subset(succ(597 ^ [648 ^ []]), 648 ^ [])), 488 : ordinal_subset(succ(597 ^ [648 ^ []]), 648 ^ []), 488 : ordinal(succ(597 ^ [648 ^ []])), 488 : ordinal(648 ^ [])],extension(480 ^ 12,bind([[_130501, _130503], [648 ^ [], succ(597 ^ [648 ^ []])]]))).
% 46.78/45.95  ncf('1.2.1.2.1.1',plain,[-(ordinal_subset(succ(597 ^ [648 ^ []]), 648 ^ [])), 554 : in(597 ^ [648 ^ []], 648 ^ []), 554 : ordinal(648 ^ []), 550 : ordinal(597 ^ [648 ^ []])],extension(546 ^ 15,bind([[_132518, _132656], [597 ^ [648 ^ []], 648 ^ []]]))).
% 46.78/45.95  ncf('1.2.1.2.1.1.1',plain,[-(in(597 ^ [648 ^ []], 648 ^ []))],extension(601 ^ 20)).
% 46.78/45.95  ncf('1.2.1.2.1.1.2',plain,[-(ordinal(648 ^ []))],lemmata('[2, 1].x')).
% 46.78/45.95  ncf('1.2.1.2.1.1.3',plain,[-(ordinal(597 ^ [648 ^ []]))],extension(599 ^ 16)).
% 46.78/45.95  ncf('1.2.1.2.1.2',plain,[-(ordinal(succ(597 ^ [648 ^ []]))), ordinal(597 ^ [648 ^ []])],extension(369 ^ 13,bind([[_127019], [597 ^ [648 ^ []]]]))).
% 46.78/45.95  ncf('1.2.1.2.1.2.1',plain,[-(ordinal(597 ^ [648 ^ []]))],extension(599 ^ 14)).
% 46.78/45.95  ncf('1.2.1.2.1.3',plain,[-(ordinal(648 ^ []))],lemmata('[2, 1].x')).
% 46.78/45.95  ncf('1.2.1.2.2',plain,[succ(597 ^ [648 ^ []]) = 648 ^ [], -(648 ^ [] = succ(597 ^ [648 ^ []]))],extension(4 ^ 12,bind([[_115641, _115643], [648 ^ [], succ(597 ^ [648 ^ []])]]))).
% 46.78/45.95  ncf('1.2.1.2.2.1',plain,[648 ^ [] = succ(597 ^ [648 ^ []]), ordinal(597 ^ [648 ^ []])],extension(656 ^ 13,bind([[_136213], [597 ^ [648 ^ []]]]))).
% 46.78/45.95  ncf('1.2.1.2.2.1.1',plain,[-(ordinal(597 ^ [648 ^ []]))],extension(599 ^ 14)).
% 46.78/45.95  ncf('1.2.1.3',plain,[-(epsilon_transitive(succ(597 ^ [648 ^ []]))), ordinal(succ(597 ^ [648 ^ []]))],extension(236 ^ 9,bind([[_122975], [succ(597 ^ [648 ^ []])]]))).
% 46.78/45.95  ncf('1.2.1.3.1',plain,[-(ordinal(succ(597 ^ [648 ^ []]))), ordinal(597 ^ [648 ^ []])],extension(369 ^ 10,bind([[_127019], [597 ^ [648 ^ []]]]))).
% 46.78/45.95  ncf('1.2.1.3.1.1',plain,[-(ordinal(597 ^ [648 ^ []]))],extension(599 ^ 11)).
% 46.78/45.95  ncf('1.2.2',plain,[-(ordinal(648 ^ []))],extension(650 ^ 4)).
% 46.78/45.95  %-----------------------------------------------------
% 46.78/45.95  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------