%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 12:02:45 EDT 2023

% Result   : Theorem 0.43s 1.39s
% Output   : Proof 0.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 13:27:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.43/1.39  
% 0.43/1.39  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.43/1.39  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/1.39  %-----------------------------------------------------
% 0.43/1.39  ncf(matrix, plain, [(521 ^ _75367) ^ [] : [-(relation(519 ^ []))], (523 ^ _75367) ^ [] : [-(function(519 ^ []))], (525 ^ _75367) ^ [] : [-(in(518 ^ [], 517 ^ []))], (527 ^ _75367) ^ [] : [apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(519 ^ [], 518 ^ [])], (98 ^ _75367) ^ [_78524, _78526, _78528, _78530] : [-(ordered_pair(_78530, _78526) = ordered_pair(_78528, _78524)), _78530 = _78528, _78526 = _78524], (108 ^ _75367) ^ [_78855, _78857] : [_78857 = _78855, -(singleton(_78857) = singleton(_78855))], (114 ^ _75367) ^ [_79101, _79103, _79105, _79107] : [-(unordered_pair(_79107, _79103) = unordered_pair(_79105, _79101)), _79107 = _79105, _79103 = _79101], (124 ^ _75367) ^ [_79460, _79462, _79464, _79466] : [-(set_intersection2(_79466, _79462) = set_intersection2(_79464, _79460)), _79466 = _79464, _79462 = _79460], (134 ^ _75367) ^ [_79791, _79793] : [_79793 = _79791, -(relation_dom(_79793) = relation_dom(_79791))], (140 ^ _75367) ^ [_80037, _80039, _80041, _80043] : [-(relation_dom_restriction(_80043, _80039) = relation_dom_restriction(_80041, _80037)), _80043 = _80041, _80039 = _80037], (150 ^ _75367) ^ [_80376, _80378, _80380, _80382] : [-(apply(_80382, _80378) = apply(_80380, _80376)), _80382 = _80380, _80378 = _80376], (2 ^ _75367) ^ [_75511] : [-(_75511 = _75511)], (4 ^ _75367) ^ [_75618, _75620] : [_75620 = _75618, -(_75618 = _75620)], (10 ^ _75367) ^ [_75822, _75824, _75826] : [-(_75826 = _75822), _75826 = _75824, _75824 = _75822], (20 ^ _75367) ^ [_76135, _76137] : [-(one_to_one(_76135)), _76137 = _76135, one_to_one(_76137)], (30 ^ _75367) ^ [_76430, _76432] : [-(relation_empty_yielding(_76430)), _76432 = _76430, relation_empty_yielding(_76432)], (40 ^ _75367) ^ [_76753, _76755, _76757, _76759] : [-(element(_76757, _76753)), element(_76759, _76755), _76759 = _76757, _76755 = _76753], (54 ^ _75367) ^ [_77169, _77171] : [-(empty(_77169)), _77171 = _77169, empty(_77171)], (64 ^ _75367) ^ [_77464, _77466] : [-(relation(_77464)), _77466 = _77464, relation(_77466)], (74 ^ _75367) ^ [_77759, _77761] : [-(function(_77759)), _77761 = _77759, function(_77761)], (84 ^ _75367) ^ [_78062, _78064, _78066, _78068] : [-(in(_78066, _78062)), in(_78068, _78064), _78068 = _78066, _78064 = _78062], (160 ^ _75367) ^ [_80733, _80735] : [in(_80735, _80733), in(_80733, _80735)], (166 ^ _75367) ^ [_80930] : [empty(_80930), -(function(_80930))], (172 ^ _75367) ^ [_81116] : [empty(_81116), -(relation(_81116))], (178 ^ _75367) ^ [_81302] : [189 ^ _75367 : [(190 ^ _75367) ^ [] : [-(relation(_81302))], (192 ^ _75367) ^ [] : [-(function(_81302))], (194 ^ _75367) ^ [] : [-(one_to_one(_81302))]], relation(_81302), empty(_81302), function(_81302)], (196 ^ _75367) ^ [_81794, _81796] : [-(unordered_pair(_81796, _81794) = unordered_pair(_81794, _81796))], (198 ^ _75367) ^ [_81894, _81896] : [-(set_intersection2(_81896, _81894) = set_intersection2(_81894, _81896))], (200 ^ _75367) ^ [_81995] : [relation(_81995), function(_81995), 207 ^ _75367 : [(208 ^ _75367) ^ [_82287, _82289] : [in(_82289, relation_dom(_81995)), 211 ^ _75367 : [(212 ^ _75367) ^ [] : [_82287 = apply(_81995, _82289), -(in(ordered_pair(_82289, _82287), _81995))], (218 ^ _75367) ^ [] : [in(ordered_pair(_82289, _82287), _81995), -(_82287 = apply(_81995, _82289))]]], (224 ^ _75367) ^ [_82739, _82741] : [-(in(_82741, relation_dom(_81995))), 227 ^ _75367 : [(228 ^ _75367) ^ [] : [_82739 = apply(_81995, _82741), -(_82739 = empty_set)], (234 ^ _75367) ^ [] : [_82739 = empty_set, -(_82739 = apply(_81995, _82741))]]]]], (240 ^ _75367) ^ [_83227, _83229] : [-(ordered_pair(_83229, _83227) = unordered_pair(unordered_pair(_83229, _83227), singleton(_83229)))], (242 ^ _75367) ^ [] : [true___, -(true___)], (248 ^ _75367) ^ [] : [true___, -(true___)], (254 ^ _75367) ^ [] : [true___, -(true___)], (260 ^ _75367) ^ [] : [true___, -(true___)], (266 ^ _75367) ^ [] : [true___, -(true___)], (272 ^ _75367) ^ [] : [true___, -(true___)], (278 ^ _75367) ^ [] : [true___, -(true___)], (284 ^ _75367) ^ [_84180, _84182] : [relation(_84182), -(relation(relation_dom_restriction(_84182, _84180)))], (290 ^ _75367) ^ [] : [true___, -(true___)], (297 ^ _75367) ^ [_84521] : [-(element(295 ^ [_84521], _84521))], (299 ^ _75367) ^ [] : [-(empty(empty_set))], (301 ^ _75367) ^ [] : [-(relation(empty_set))], (303 ^ _75367) ^ [] : [-(relation_empty_yielding(empty_set))], (305 ^ _75367) ^ [_84796, _84798] : [312 ^ _75367 : [(313 ^ _75367) ^ [] : [-(relation(relation_dom_restriction(_84798, _84796)))], (315 ^ _75367) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_84798, _84796)))]], relation(_84798), relation_empty_yielding(_84798)], (317 ^ _75367) ^ [_85174, _85176] : [-(relation(set_intersection2(_85176, _85174))), relation(_85176), relation(_85174)], (327 ^ _75367) ^ [] : [-(empty(empty_set))], (329 ^ _75367) ^ [_85510, _85512] : [empty(ordered_pair(_85512, _85510))], (331 ^ _75367) ^ [_85591] : [empty(singleton(_85591))], (333 ^ _75367) ^ [_85683, _85685] : [empty(unordered_pair(_85685, _85683))], (335 ^ _75367) ^ [_85794, _85796] : [342 ^ _75367 : [(343 ^ _75367) ^ [] : [-(relation(relation_dom_restriction(_85796, _85794)))], (345 ^ _75367) ^ [] : [-(function(relation_dom_restriction(_85796, _85794)))]], relation(_85796), function(_85796)], (347 ^ _75367) ^ [] : [-(empty(empty_set))], (349 ^ _75367) ^ [] : [-(relation(empty_set))], (351 ^ _75367) ^ [_86266] : [empty(relation_dom(_86266)), -(empty(_86266)), relation(_86266)], (361 ^ _75367) ^ [_86543] : [empty(_86543), 364 ^ _75367 : [(365 ^ _75367) ^ [] : [-(empty(relation_dom(_86543)))], (367 ^ _75367) ^ [] : [-(relation(relation_dom(_86543)))]]], (369 ^ _75367) ^ [_86807, _86809] : [-(set_intersection2(_86809, _86809) = _86809)], (371 ^ _75367) ^ [_86933, _86935, _86937] : [relation(_86933), function(_86933), 378 ^ _75367 : [(379 ^ _75367) ^ [] : [in(_86935, relation_dom(relation_dom_restriction(_86933, _86937))), 382 ^ _75367 : [(383 ^ _75367) ^ [] : [-(in(_86935, relation_dom(_86933)))], (385 ^ _75367) ^ [] : [-(in(_86935, _86937))]]], (387 ^ _75367) ^ [] : [-(in(_86935, relation_dom(relation_dom_restriction(_86933, _86937)))), in(_86935, relation_dom(_86933)), in(_86935, _86937)]]], (398 ^ _75367) ^ [] : [-(relation(396 ^ []))], (400 ^ _75367) ^ [] : [-(function(396 ^ []))], (403 ^ _75367) ^ [] : [-(empty(401 ^ []))], (405 ^ _75367) ^ [] : [-(relation(401 ^ []))], (408 ^ _75367) ^ [] : [-(empty(406 ^ []))], (411 ^ _75367) ^ [] : [-(relation(409 ^ []))], (413 ^ _75367) ^ [] : [-(empty(409 ^ []))], (415 ^ _75367) ^ [] : [-(function(409 ^ []))], (418 ^ _75367) ^ [] : [empty(416 ^ [])], (420 ^ _75367) ^ [] : [-(relation(416 ^ []))], (423 ^ _75367) ^ [] : [empty(421 ^ [])], (426 ^ _75367) ^ [] : [-(relation(424 ^ []))], (428 ^ _75367) ^ [] : [-(function(424 ^ []))], (430 ^ _75367) ^ [] : [-(one_to_one(424 ^ []))], (433 ^ _75367) ^ [] : [-(relation(431 ^ []))], (435 ^ _75367) ^ [] : [-(relation_empty_yielding(431 ^ []))], (437 ^ _75367) ^ [_88879, _88881] : [in(_88881, _88879), -(element(_88881, _88879))], (443 ^ _75367) ^ [_89060] : [-(set_intersection2(_89060, empty_set) = empty_set)], (445 ^ _75367) ^ [_89170, _89172] : [element(_89172, _89170), -(empty(_89170)), -(in(_89172, _89170))], (496 ^ _75367) ^ [_90843] : [empty(_90843), -(_90843 = empty_set)], (502 ^ _75367) ^ [_91045, _91047] : [in(_91047, _91045), empty(_91045)], (508 ^ _75367) ^ [_91232, _91234] : [empty(_91234), -(_91234 = _91232), empty(_91232)], (455 ^ _75367) ^ [_89468, _89470] : [relation(_89468), function(_89468), 462 ^ _75367 : [(463 ^ _75367) ^ [_89735] : [relation(_89735), function(_89735), 470 ^ _75367 : [(471 ^ _75367) ^ [] : [_89468 = relation_dom_restriction(_89735, _89470), 474 ^ _75367 : [(475 ^ _75367) ^ [] : [-(relation_dom(_89468) = set_intersection2(relation_dom(_89735), _89470))], (477 ^ _75367) ^ [_90189] : [in(_90189, relation_dom(_89468)), -(apply(_89468, _90189) = apply(_89735, _90189))]]], (483 ^ _75367) ^ [] : [-(_89468 = relation_dom_restriction(_89735, _89470)), relation_dom(_89468) = set_intersection2(relation_dom(_89735), _89470), 489 ^ _75367 : [(490 ^ _75367) ^ [] : [-(in(488 ^ [_89468, _89470, _89735], relation_dom(_89468)))], (492 ^ _75367) ^ [] : [apply(_89468, 488 ^ [_89468, _89470, _89735]) = apply(_89735, 488 ^ [_89468, _89470, _89735])]]]]]]]], input).
% 0.43/1.39  ncf('1',plain,[apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(519 ^ [], 518 ^ [])],start(527 ^ 0)).
% 0.43/1.39  ncf('1.1',plain,[-(apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(519 ^ [], 518 ^ [])), 477 : in(518 ^ [], relation_dom(relation_dom_restriction(519 ^ [], 517 ^ []))), 477 : relation_dom_restriction(519 ^ [], 517 ^ []) = relation_dom_restriction(519 ^ [], 517 ^ []), 471 : relation(519 ^ []), 471 : function(519 ^ []), 463 : relation(relation_dom_restriction(519 ^ [], 517 ^ [])), 463 : function(relation_dom_restriction(519 ^ [], 517 ^ []))],extension(455 ^ 1,bind([[_89468, _89470, _89735, _90189], [relation_dom_restriction(519 ^ [], 517 ^ []), 517 ^ [], 519 ^ [], 518 ^ []]]))).
% 0.43/1.39  ncf('1.1.1',plain,[-(in(518 ^ [], relation_dom(relation_dom_restriction(519 ^ [], 517 ^ [])))), 228 : apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []), 228 : -(apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = empty_set), 224 : relation(relation_dom_restriction(519 ^ [], 517 ^ [])), 224 : function(relation_dom_restriction(519 ^ [], 517 ^ []))],extension(200 ^ 8,bind([[_81995, _82739, _82741], [relation_dom_restriction(519 ^ [], 517 ^ []), apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []), 518 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.1',plain,[-(apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ [])), relation_dom_restriction(519 ^ [], 517 ^ []) = relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ [] = 518 ^ []],extension(150 ^ 13,bind([[_80376, _80378, _80380, _80382], [518 ^ [], 518 ^ [], relation_dom_restriction(519 ^ [], 517 ^ []), relation_dom_restriction(519 ^ [], 517 ^ [])]]))).
% 0.43/1.39  ncf('1.1.1.1.1',plain,[-(relation_dom_restriction(519 ^ [], 517 ^ []) = relation_dom_restriction(519 ^ [], 517 ^ []))],extension(2 ^ 14,bind([[_75511], [relation_dom_restriction(519 ^ [], 517 ^ [])]]))).
% 0.43/1.39  ncf('1.1.1.1.2',plain,[-(518 ^ [] = 518 ^ [])],extension(2 ^ 14,bind([[_75511], [518 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.2',plain,[apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = empty_set, 234 : -(apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(519 ^ [], 518 ^ [])), 234 : -(in(518 ^ [], relation_dom(519 ^ []))), 224 : relation(519 ^ []), 224 : function(519 ^ [])],extension(200 ^ 13,bind([[_81995, _82739, _82741], [519 ^ [], apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []), 518 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.2.1',plain,[apply(relation_dom_restriction(519 ^ [], 517 ^ []), 518 ^ []) = apply(519 ^ [], 518 ^ [])],reduction('1')).
% 0.43/1.39  ncf('1.1.1.2.2',plain,[in(518 ^ [], relation_dom(519 ^ [])), 387 : -(in(518 ^ [], relation_dom(relation_dom_restriction(519 ^ [], 517 ^ [])))), 387 : in(518 ^ [], 517 ^ []), 387 : relation(519 ^ []), 387 : function(519 ^ [])],extension(371 ^ 16,bind([[_86933, _86935, _86937], [519 ^ [], 518 ^ [], 517 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.2.2.1',plain,[in(518 ^ [], relation_dom(relation_dom_restriction(519 ^ [], 517 ^ [])))],reduction('1.1')).
% 0.43/1.39  ncf('1.1.1.2.2.2',plain,[-(in(518 ^ [], 517 ^ []))],extension(525 ^ 19)).
% 0.43/1.39  ncf('1.1.1.2.2.3',plain,[-(relation(519 ^ []))],extension(521 ^ 17)).
% 0.43/1.39  ncf('1.1.1.2.2.4',plain,[-(function(519 ^ []))],extension(523 ^ 17)).
% 0.43/1.39  ncf('1.1.1.2.3',plain,[-(relation(519 ^ []))],extension(521 ^ 14)).
% 0.43/1.39  ncf('1.1.1.2.4',plain,[-(function(519 ^ []))],extension(523 ^ 14)).
% 0.43/1.39  ncf('1.1.1.3',plain,[-(relation(relation_dom_restriction(519 ^ [], 517 ^ []))), relation(519 ^ [])],extension(284 ^ 9,bind([[_84180, _84182], [517 ^ [], 519 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.3.1',plain,[-(relation(519 ^ []))],extension(521 ^ 10)).
% 0.43/1.39  ncf('1.1.1.4',plain,[-(function(relation_dom_restriction(519 ^ [], 517 ^ []))), relation(519 ^ []), function(519 ^ [])],extension(335 ^ 9,bind([[_85794, _85796], [517 ^ [], 519 ^ []]]))).
% 0.43/1.39  ncf('1.1.1.4.1',plain,[-(relation(519 ^ []))],extension(521 ^ 10)).
% 0.43/1.39  ncf('1.1.1.4.2',plain,[-(function(519 ^ []))],extension(523 ^ 10)).
% 0.43/1.39  ncf('1.1.2',plain,[-(relation_dom_restriction(519 ^ [], 517 ^ []) = relation_dom_restriction(519 ^ [], 517 ^ [])), 519 ^ [] = 519 ^ [], 517 ^ [] = 517 ^ []],extension(140 ^ 6,bind([[_80037, _80039, _80041, _80043], [517 ^ [], 517 ^ [], 519 ^ [], 519 ^ []]]))).
% 0.43/1.39  ncf('1.1.2.1',plain,[-(519 ^ [] = 519 ^ [])],extension(2 ^ 7,bind([[_75511], [519 ^ []]]))).
% 0.43/1.39  ncf('1.1.2.2',plain,[-(517 ^ [] = 517 ^ [])],extension(2 ^ 7,bind([[_75511], [517 ^ []]]))).
% 0.43/1.39  ncf('1.1.3',plain,[-(relation(519 ^ []))],extension(521 ^ 4)).
% 0.43/1.39  ncf('1.1.4',plain,[-(function(519 ^ []))],extension(523 ^ 4)).
% 0.43/1.39  ncf('1.1.5',plain,[-(relation(relation_dom_restriction(519 ^ [], 517 ^ []))), relation(519 ^ [])],extension(284 ^ 2,bind([[_84180, _84182], [517 ^ [], 519 ^ []]]))).
% 0.43/1.39  ncf('1.1.5.1',plain,[-(relation(519 ^ []))],extension(521 ^ 3)).
% 0.43/1.39  ncf('1.1.6',plain,[-(function(relation_dom_restriction(519 ^ [], 517 ^ []))), relation(519 ^ []), function(519 ^ [])],extension(335 ^ 2,bind([[_85794, _85796], [517 ^ [], 519 ^ []]]))).
% 0.43/1.39  ncf('1.1.6.1',plain,[-(relation(519 ^ []))],extension(521 ^ 3)).
% 0.43/1.39  ncf('1.1.6.2',plain,[-(function(519 ^ []))],extension(523 ^ 3)).
% 0.43/1.39  %-----------------------------------------------------
% 0.43/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------