%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM409+1 : 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 11:44:32 EDT 2023

% Result   : Theorem 43.35s 42.79s
% Output   : Proof 43.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n022.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 17:47:47 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 43.35/42.79  
% 43.35/42.79  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 43.35/42.79  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.35/42.79  %-----------------------------------------------------
% 43.35/42.79  ncf(matrix, plain, [(658 ^ _120627) ^ [] : [transfinite_sequence_of(empty_set, 656 ^ [])], !, (547 ^ _99764) ^ [] : [-(relation(545 ^ []))], (224 ^ _99764) ^ [_106899, _106901] : [_106901 = _106899, -(relation_rng(_106901) = relation_rng(_106899))], (236 ^ _99764) ^ [_107368] : [empty(_107368), -(function(_107368))], (485 ^ _99764) ^ [] : [-(ordinal(479 ^ []))], (478 ^ _99764) ^ [] : [-(function(474 ^ []))], (4 ^ _99764) ^ [_99995, _99997] : [_99997 = _99995, -(_99995 = _99997)], (535 ^ _99764) ^ [] : [-(epsilon_transitive(531 ^ []))], (530 ^ _99764) ^ [] : [-(one_to_one(524 ^ []))], (513 ^ _99764) ^ [] : [-(epsilon_connected(501 ^ []))], (212 ^ _99764) ^ [_106483, _106485] : [_106485 = _106483, -(powerset(_106485) = powerset(_106483))], (403 ^ _99764) ^ [_112698, _112700] : [empty(ordered_pair(_112700, _112698))], (256 ^ _99764) ^ [_107997] : [267 ^ _99764 : [(272 ^ _99764) ^ [] : [-(one_to_one(_107997))], (270 ^ _99764) ^ [] : [-(function(_107997))], (268 ^ _99764) ^ [] : [-(relation(_107997))]], relation(_107997), empty(_107997), function(_107997)], (449 ^ _99764) ^ [_113974] : [empty(relation_rng(_113974)), -(empty(_113974)), relation(_113974)], (407 ^ _99764) ^ [] : [-(relation_empty_yielding(empty_set))], (526 ^ _99764) ^ [] : [-(relation(524 ^ []))], (511 ^ _99764) ^ [] : [-(epsilon_transitive(501 ^ []))], (515 ^ _99764) ^ [] : [-(ordinal(501 ^ []))], (411 ^ _99764) ^ [] : [-(one_to_one(empty_set))], (500 ^ _99764) ^ [] : [-(function(494 ^ []))], (242 ^ _99764) ^ [_107554] : [ordinal(_107554), 245 ^ _99764 : [(248 ^ _99764) ^ [] : [-(epsilon_connected(_107554))], (246 ^ _99764) ^ [] : [-(epsilon_transitive(_107554))]]], (503 ^ _99764) ^ [] : [-(relation(501 ^ []))], (563 ^ _99764) ^ [] : [-(relation_non_empty(559 ^ []))], (202 ^ _99764) ^ [_106152, _106154, _106156, _106158] : [-(ordered_pair(_106158, _106154) = ordered_pair(_106156, _106152)), _106158 = _106156, _106154 = _106152], (498 ^ _99764) ^ [] : [-(empty(494 ^ []))], (483 ^ _99764) ^ [] : [-(epsilon_connected(479 ^ []))], (162 ^ _99764) ^ [_104794, _104796] : [-(empty(_104794)), _104796 = _104794, empty(_104796)], (599 ^ _99764) ^ [_118649, _118651, _118653] : [-(element(_118653, _118649)), in(_118653, _118651), element(_118651, powerset(_118649))], (196 ^ _99764) ^ [_105906, _105908] : [_105908 = _105906, -(singleton(_105908) = singleton(_105906))], (296 ^ _99764) ^ [_109186] : [relation(_109186), 299 ^ _99764 : [(300 ^ _99764) ^ [_109367] : [_109367 = relation_dom(_109186), 303 ^ _99764 : [(311 ^ _99764) ^ [_109791] : [312 ^ _99764 : [(313 ^ _99764) ^ [_109870] : [in(ordered_pair(_109791, _109870), _109186)]], -(in(_109791, _109367))], (304 ^ _99764) ^ [_109547] : [in(_109547, _109367), -(in(ordered_pair(_109547, 307 ^ [_109186, _109367, _109547]), _109186))]]], (317 ^ _99764) ^ [_109998] : [-(_109998 = relation_dom(_109186)), 321 ^ _99764 : [(324 ^ _99764) ^ [_110261] : [in(ordered_pair(318 ^ [_109186, _109998], _110261), _109186)], (322 ^ _99764) ^ [] : [-(in(318 ^ [_109186, _109998], _109998))]], 326 ^ _99764 : [(329 ^ _99764) ^ [] : [in(318 ^ [_109186, _109998], _109998)], (327 ^ _99764) ^ [] : [-(in(ordered_pair(318 ^ [_109186, _109998], 325 ^ [_109186, _109998]), _109186))]]]]], (90 ^ _99764) ^ [_102577, _102579] : [-(relation_non_empty(_102577)), _102579 = _102577, relation_non_empty(_102579)], (148 ^ _99764) ^ [_104378, _104380, _104382, _104384] : [-(in(_104382, _104378)), in(_104384, _104380), _104384 = _104382, _104380 = _104378], (496 ^ _99764) ^ [] : [-(relation(494 ^ []))], (30 ^ _99764) ^ [_100807, _100809] : [-(one_to_one(_100807)), _100809 = _100807, one_to_one(_100809)], (533 ^ _99764) ^ [] : [empty(531 ^ [])], (549 ^ _99764) ^ [] : [-(relation_empty_yielding(545 ^ []))], (333 ^ _99764) ^ [_110626, _110628] : [-(ordered_pair(_110628, _110626) = unordered_pair(unordered_pair(_110628, _110626), singleton(_110628)))], (509 ^ _99764) ^ [] : [-(empty(501 ^ []))], (520 ^ _99764) ^ [] : [-(relation(516 ^ []))], (425 ^ _99764) ^ [_113341] : [empty(relation_dom(_113341)), -(empty(_113341)), relation(_113341)], (355 ^ _99764) ^ [_111259, _111261] : [relation(_111259), function(_111259), transfinite_sequence(_111259), 366 ^ _99764 : [(373 ^ _99764) ^ [] : [subset(relation_rng(_111259), _111261), -(transfinite_sequence_of(_111259, _111261))], (367 ^ _99764) ^ [] : [transfinite_sequence_of(_111259, _111261), -(subset(relation_rng(_111259), _111261))]]], (138 ^ _99764) ^ [_104055, _104057] : [-(relation(_104055)), _104057 = _104055, relation(_104057)], (476 ^ _99764) ^ [] : [-(relation(474 ^ []))], (467 ^ _99764) ^ [_114516] : [empty(_114516), 470 ^ _99764 : [(473 ^ _99764) ^ [] : [-(relation(relation_rng(_114516)))], (471 ^ _99764) ^ [] : [-(empty(relation_rng(_114516)))]]], (561 ^ _99764) ^ [] : [-(relation(559 ^ []))], (554 ^ _99764) ^ [] : [-(relation(552 ^ []))], (647 ^ _99764) ^ [_120101, _120103] : [empty(_120103), -(_120103 = _120101), empty(_120101)], (528 ^ _99764) ^ [] : [-(function(524 ^ []))], (40 ^ _99764) ^ [_101102, _101104] : [-(epsilon_transitive(_101102)), _101104 = _101102, epsilon_transitive(_101104)], (60 ^ _99764) ^ [_101692, _101694] : [-(ordinal(_101692)), _101694 = _101692, ordinal(_101694)], (518 ^ _99764) ^ [] : [empty(516 ^ [])], (379 ^ _99764) ^ [_111901, _111903] : [transfinite_sequence_of(_111901, _111903), 382 ^ _99764 : [(387 ^ _99764) ^ [] : [-(transfinite_sequence(_111901))], (385 ^ _99764) ^ [] : [-(function(_111901))], (383 ^ _99764) ^ [] : [-(relation(_111901))]]], (405 ^ _99764) ^ [] : [-(relation(empty_set))], (523 ^ _99764) ^ [] : [empty(521 ^ [])], (294 ^ _99764) ^ [_109085, _109087] : [-(unordered_pair(_109087, _109085) = unordered_pair(_109085, _109087))], (593 ^ _99764) ^ [_118419, _118421] : [subset(_118421, _118419), -(element(_118421, powerset(_118419)))], (565 ^ _99764) ^ [] : [-(function(559 ^ []))], (569 ^ _99764) ^ [_117638, _117640] : [in(_117640, _117638), -(element(_117640, _117638))], (80 ^ _99764) ^ [_102282, _102284] : [-(transfinite_sequence(_102282)), _102284 = _102282, transfinite_sequence(_102284)], (556 ^ _99764) ^ [] : [-(function(552 ^ []))], (641 ^ _99764) ^ [_119914, _119916] : [in(_119916, _119914), empty(_119914)], (459 ^ _99764) ^ [_114251] : [empty(_114251), 462 ^ _99764 : [(465 ^ _99764) ^ [] : [-(relation(relation_dom(_114251)))], (463 ^ _99764) ^ [] : [-(empty(relation_dom(_114251)))]]], (505 ^ _99764) ^ [] : [-(function(501 ^ []))], (401 ^ _99764) ^ [] : [-(empty(empty_set))], (2 ^ _99764) ^ [_99888] : [-(_99888 = _99888)], (409 ^ _99764) ^ [] : [-(function(empty_set))], (10 ^ _99764) ^ [_100199, _100201, _100203] : [-(_100203 = _100199), _100203 = _100201, _100201 = _100199], (575 ^ _99764) ^ [_117848, _117850] : [element(_117850, _117848), -(empty(_117848)), -(in(_117850, _117848))], (635 ^ _99764) ^ [_119712] : [empty(_119712), -(_119712 = empty_set)], (335 ^ _99764) ^ [_110732] : [relation(_110732), function(_110732), 342 ^ _99764 : [(349 ^ _99764) ^ [] : [ordinal(relation_dom(_110732)), -(transfinite_sequence(_110732))], (343 ^ _99764) ^ [] : [transfinite_sequence(_110732), -(ordinal(relation_dom(_110732)))]]], (20 ^ _99764) ^ [_100512, _100514] : [-(with_non_empty_elements(_100512)), _100514 = _100512, with_non_empty_elements(_100514)], (393 ^ _99764) ^ [_112386] : [-(element(391 ^ [_112386], _112386))], (230 ^ _99764) ^ [_107171, _107173] : [in(_107173, _107171), in(_107171, _107173)], (542 ^ _99764) ^ [] : [-(relation(540 ^ []))], (100 ^ _99764) ^ [_102872, _102874] : [-(function(_102872)), _102874 = _102872, function(_102874)], (481 ^ _99764) ^ [] : [-(epsilon_transitive(479 ^ []))], (419 ^ _99764) ^ [] : [-(ordinal(empty_set))], (415 ^ _99764) ^ [] : [-(epsilon_transitive(empty_set))], (551 ^ _99764) ^ [] : [-(function(545 ^ []))], (421 ^ _99764) ^ [] : [-(empty(empty_set))], (110 ^ _99764) ^ [_103195, _103197, _103199, _103201] : [-(subset(_103199, _103195)), subset(_103201, _103197), _103201 = _103199, _103197 = _103195], (488 ^ _99764) ^ [] : [-(empty(486 ^ []))], (284 ^ _99764) ^ [_108759] : [empty(_108759), 287 ^ _99764 : [(292 ^ _99764) ^ [] : [-(ordinal(_108759))], (290 ^ _99764) ^ [] : [-(epsilon_connected(_108759))], (288 ^ _99764) ^ [] : [-(epsilon_transitive(_108759))]]], (186 ^ _99764) ^ [_105575, _105577, _105579, _105581] : [-(unordered_pair(_105581, _105577) = unordered_pair(_105579, _105575)), _105581 = _105579, _105577 = _105575], (413 ^ _99764) ^ [] : [-(empty(empty_set))], (397 ^ _99764) ^ [] : [-(relation(empty_set))], (390 ^ _99764) ^ [_112264] : [-(transfinite_sequence_of(388 ^ [_112264], _112264))], (507 ^ _99764) ^ [] : [-(one_to_one(501 ^ []))], (172 ^ _99764) ^ [_105097, _105099, _105101, _105103] : [-(transfinite_sequence_of(_105101, _105097)), transfinite_sequence_of(_105103, _105099), _105103 = _105101, _105099 = _105097], (250 ^ _99764) ^ [_107811] : [empty(_107811), -(relation(_107811))], (587 ^ _99764) ^ [_118253, _118255] : [element(_118255, powerset(_118253)), -(subset(_118255, _118253))], (609 ^ _99764) ^ [_118976, _118978, _118980] : [in(_118980, _118978), element(_118978, powerset(_118976)), empty(_118976)], (544 ^ _99764) ^ [] : [-(relation_empty_yielding(540 ^ []))], (585 ^ _99764) ^ [_118117] : [-(subset(empty_set, _118117))], (395 ^ _99764) ^ [] : [-(empty(empty_set))], (274 ^ _99764) ^ [_108490] : [-(ordinal(_108490)), epsilon_transitive(_108490), epsilon_connected(_108490)], (435 ^ _99764) ^ [_113618] : [-(with_non_empty_elements(relation_rng(_113618))), relation(_113618), relation_non_empty(_113618), function(_113618)], (399 ^ _99764) ^ [] : [-(relation_empty_yielding(empty_set))], (70 ^ _99764) ^ [_101987, _101989] : [-(relation_empty_yielding(_101987)), _101989 = _101987, relation_empty_yielding(_101989)], (537 ^ _99764) ^ [] : [-(epsilon_connected(531 ^ []))], (558 ^ _99764) ^ [] : [-(transfinite_sequence(552 ^ []))], (124 ^ _99764) ^ [_103639, _103641, _103643, _103645] : [-(element(_103643, _103639)), element(_103645, _103641), _103645 = _103643, _103641 = _103639], (539 ^ _99764) ^ [] : [-(ordinal(531 ^ []))], (619 ^ _99764) ^ [_119272] : [relation(_119272), 622 ^ _99764 : [(629 ^ _99764) ^ [] : [relation_rng(_119272) = empty_set, -(relation_dom(_119272) = empty_set)], (623 ^ _99764) ^ [] : [relation_dom(_119272) = empty_set, -(relation_rng(_119272) = empty_set)]]], (50 ^ _99764) ^ [_101397, _101399] : [-(epsilon_connected(_101397)), _101399 = _101397, epsilon_connected(_101399)], (493 ^ _99764) ^ [] : [-(empty(491 ^ []))], (490 ^ _99764) ^ [] : [-(relation(486 ^ []))], (218 ^ _99764) ^ [_106701, _106703] : [_106703 = _106701, -(relation_dom(_106703) = relation_dom(_106701))], (423 ^ _99764) ^ [] : [-(relation(empty_set))], (417 ^ _99764) ^ [] : [-(epsilon_connected(empty_set))], (567 ^ _99764) ^ [_117529, _117531] : [-(subset(_117531, _117531))]], input).
% 43.35/42.79  ncf('1',plain,[transfinite_sequence_of(empty_set, 656 ^ [])],start(658 ^ 0)).
% 43.35/42.79  ncf('1.1',plain,[-(transfinite_sequence_of(empty_set, 656 ^ [])), 373 : subset(relation_rng(empty_set), 656 ^ []), 373 : relation(empty_set), 373 : function(empty_set), 373 : transfinite_sequence(empty_set)],extension(355 ^ 1,bind([[_111259, _111261], [empty_set, 656 ^ []]]))).
% 43.35/42.79  ncf('1.1.1',plain,[-(subset(relation_rng(empty_set), 656 ^ [])), element(relation_rng(empty_set), powerset(656 ^ []))],extension(587 ^ 4,bind([[_118253, _118255], [656 ^ [], relation_rng(empty_set)]]))).
% 43.35/42.79  ncf('1.1.1.1',plain,[-(element(relation_rng(empty_set), powerset(656 ^ []))), element(empty_set, powerset(656 ^ [])), empty_set = relation_rng(empty_set), powerset(656 ^ []) = powerset(656 ^ [])],extension(124 ^ 5,bind([[_103639, _103641, _103643, _103645], [powerset(656 ^ []), powerset(656 ^ []), relation_rng(empty_set), empty_set]]))).
% 43.35/42.79  ncf('1.1.1.1.1',plain,[-(element(empty_set, powerset(656 ^ []))), subset(empty_set, 656 ^ [])],extension(593 ^ 6,bind([[_118419, _118421], [656 ^ [], empty_set]]))).
% 43.35/42.79  ncf('1.1.1.1.1.1',plain,[-(subset(empty_set, 656 ^ []))],extension(585 ^ 7,bind([[_118117], [656 ^ []]]))).
% 43.35/42.79  ncf('1.1.1.1.2',plain,[-(empty_set = relation_rng(empty_set)), empty(empty_set), empty(relation_rng(empty_set))],extension(647 ^ 6,bind([[_120101, _120103], [relation_rng(empty_set), empty_set]]))).
% 43.35/42.79  ncf('1.1.1.1.2.1',plain,[-(empty(empty_set))],extension(401 ^ 7)).
% 43.35/42.79  ncf('1.1.1.1.2.2',plain,[-(empty(relation_rng(empty_set))), empty(empty_set)],extension(467 ^ 7,bind([[_114516], [empty_set]]))).
% 43.35/42.79  ncf('1.1.1.1.2.2.1',plain,[-(empty(empty_set))],lemmata('[1, 1, 1, 1].x')).
% 43.35/42.79  ncf('1.1.1.1.3',plain,[-(powerset(656 ^ []) = powerset(656 ^ [])), powerset(656 ^ []) = powerset(656 ^ [])],extension(4 ^ 6,bind([[_99995, _99997], [powerset(656 ^ []), powerset(656 ^ [])]]))).
% 43.35/42.79  ncf('1.1.1.1.3.1',plain,[-(powerset(656 ^ []) = powerset(656 ^ []))],extension(2 ^ 7,bind([[_99888], [powerset(656 ^ [])]]))).
% 43.35/42.79  ncf('1.1.2',plain,[-(relation(empty_set)), relation_dom(494 ^ []) = empty_set, relation(relation_dom(494 ^ []))],extension(138 ^ 2,bind([[_104055, _104057], [empty_set, relation_dom(494 ^ [])]]))).
% 43.35/42.79  ncf('1.1.2.1',plain,[-(relation_dom(494 ^ []) = empty_set), empty_set = relation_dom(494 ^ [])],extension(4 ^ 3,bind([[_99995, _99997], [relation_dom(494 ^ []), empty_set]]))).
% 43.35/42.79  ncf('1.1.2.1.1',plain,[-(empty_set = relation_dom(494 ^ [])), 322 : -(in(318 ^ [494 ^ [], empty_set], empty_set)), 327 : -(in(ordered_pair(318 ^ [494 ^ [], empty_set], 325 ^ [494 ^ [], empty_set]), 494 ^ [])), 317 : relation(494 ^ [])],extension(296 ^ 4,bind([[_109186, _109998], [494 ^ [], empty_set]]))).
% 43.35/42.79  ncf('1.1.2.1.1.1',plain,[in(318 ^ [494 ^ [], empty_set], empty_set), empty(empty_set)],extension(641 ^ 9,bind([[_119914, _119916], [empty_set, 318 ^ [494 ^ [], empty_set]]]))).
% 43.35/42.79  ncf('1.1.2.1.1.1.1',plain,[-(empty(empty_set))],extension(401 ^ 10)).
% 43.35/42.79  ncf('1.1.2.1.1.2',plain,[in(ordered_pair(318 ^ [494 ^ [], empty_set], 325 ^ [494 ^ [], empty_set]), 494 ^ []), empty(494 ^ [])],extension(641 ^ 9,bind([[_119914, _119916], [494 ^ [], ordered_pair(318 ^ [494 ^ [], empty_set], 325 ^ [494 ^ [], empty_set])]]))).
% 43.35/42.79  ncf('1.1.2.1.1.2.1',plain,[-(empty(494 ^ []))],extension(498 ^ 10)).
% 43.35/42.79  ncf('1.1.2.1.1.3',plain,[-(relation(494 ^ []))],extension(496 ^ 5)).
% 43.35/42.79  ncf('1.1.2.2',plain,[-(relation(relation_dom(494 ^ []))), empty(494 ^ [])],extension(459 ^ 3,bind([[_114251], [494 ^ []]]))).
% 43.35/42.79  ncf('1.1.2.2.1',plain,[-(empty(494 ^ []))],extension(498 ^ 4)).
% 43.35/42.79  ncf('1.1.3',plain,[-(function(empty_set)), empty(empty_set)],extension(236 ^ 2,bind([[_107368], [empty_set]]))).
% 43.35/42.79  ncf('1.1.3.1',plain,[-(empty(empty_set))],extension(401 ^ 3)).
% 43.35/42.79  ncf('1.1.4',plain,[-(transfinite_sequence(empty_set)), 349 : ordinal(relation_dom(empty_set)), 349 : relation(empty_set), 349 : function(empty_set)],extension(335 ^ 2,bind([[_110732], [empty_set]]))).
% 43.35/42.79  ncf('1.1.4.1',plain,[-(ordinal(relation_dom(empty_set))), empty(relation_dom(empty_set))],extension(284 ^ 5,bind([[_108759], [relation_dom(empty_set)]]))).
% 43.35/42.79  ncf('1.1.4.1.1',plain,[-(empty(relation_dom(empty_set))), empty(empty_set)],extension(459 ^ 6,bind([[_114251], [empty_set]]))).
% 43.35/42.79  ncf('1.1.4.1.1.1',plain,[-(empty(empty_set))],extension(401 ^ 7)).
% 43.35/42.79  ncf('1.1.4.2',plain,[-(relation(empty_set))],lemmata('[1].x')).
% 43.35/42.79  ncf('1.1.4.3',plain,[-(function(empty_set))],lemmata('[1].x')).
% 43.35/42.79  %-----------------------------------------------------
% 43.35/42.79  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------